# Challenging one..!!!(help please) - combinations

#### the_storm

##### New Member
Good day experts,

This is my first question in this forum and I am optimistic to find the perfect solution here in MrExcel J ….. My question is about formulating combinations.

Imagine that I have 3 different production lines (1, 2 & 3) and I want to find all the possible combination between those production lines to evaluate what is more economical combination. These combinations will vary from no combination to all together.

The solution of the three production lines (1,2 & 3) will be as follows:
<TABLE class=MsoNormalTable style="MARGIN: auto auto auto 4.65pt; WIDTH: 207.75pt; BORDER-COLLAPSE: collapse; mso-yfti-tbllook: 1184; mso-padding-alt: 0in 5.4pt 0in 5.4pt" cellSpacing=0 cellPadding=0 width=277 border=0><TBODY><TR style="HEIGHT: 16.5pt; mso-yfti-irow: 0; mso-yfti-firstrow: yes"><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 48pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 16.5pt; BACKGROUND-COLOR: transparent; mso-border-alt: solid windowtext .5pt" noWrap width=64>
#<?xml:namespace prefix = o ns = "urn:schemas-microsoft-comfficeffice" /><o></o>

</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #f0f0f0; WIDTH: 79.9pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 16.5pt; BACKGROUND-COLOR: transparent; mso-border-top-alt: solid windowtext .5pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt" noWrap width=107>
Combinations<o></o>

</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #f0f0f0; WIDTH: 79.85pt; PADDING-TOP: 0in; BORDER-BOTTOM: #f0f0f0; HEIGHT: 16.5pt; BACKGROUND-COLOR: transparent; mso-border-top-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt" noWrap width=106>
Mix<o></o>

</TD></TR><TR style="HEIGHT: 15.75pt; mso-yfti-irow: 1"><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 48pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15.75pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt" noWrap width=64>
1<o></o>

</TD><TD style="BORDER-RIGHT: #f0f0f0; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #f0f0f0; WIDTH: 79.9pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15.75pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt" noWrap width=107>
1,2,3<o></o>

</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; BACKGROUND: #c2d69a; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 79.85pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15.75pt" noWrap width=106>
No combinations<o></o>

</TD></TR><TR style="HEIGHT: 15pt; mso-yfti-irow: 2"><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 48pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt" noWrap width=64>
2<o></o>

</TD><TD style="BORDER-RIGHT: #f0f0f0; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #f0f0f0; WIDTH: 79.9pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt" noWrap width=107>
1,23<o></o>

</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; BACKGROUND: #ffc000; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 79.85pt; PADDING-TOP: 0in; BORDER-BOTTOM: black 1pt solid; HEIGHT: 15pt" width=106 rowSpan=3>
1-2 or 2-1<o></o>

</TD></TR><TR style="HEIGHT: 15pt; mso-yfti-irow: 3"><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 48pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt" noWrap width=64>
3<o></o>

</TD><TD style="BORDER-RIGHT: #f0f0f0; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #f0f0f0; WIDTH: 79.9pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt" noWrap width=107>
2,13<o></o>

</TD></TR><TR style="HEIGHT: 15.75pt; mso-yfti-irow: 4"><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 48pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15.75pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt" noWrap width=64>
4<o></o>

</TD><TD style="BORDER-RIGHT: #f0f0f0; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #f0f0f0; WIDTH: 79.9pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15.75pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt" noWrap width=107>
3,12<o></o>

</TD></TR><TR style="HEIGHT: 15.75pt; mso-yfti-irow: 5; mso-yfti-lastrow: yes"><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 48pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15.75pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt" noWrap width=64>
5<o></o>

</TD><TD style="BORDER-RIGHT: #f0f0f0; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #f0f0f0; WIDTH: 79.9pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15.75pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt" noWrap width=107>
123<o></o>

</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; BACKGROUND: #00b0f0; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 79.85pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15.75pt" width=106>
All together<o></o>

</TD></TR></TBODY></TABLE>​
<o></o>
If there is a 4 production lines (1,2,3 & 4) the solution will be as follows:
<TABLE class=MsoNormalTable style="MARGIN: auto auto auto 4.75pt; WIDTH: 207.65pt; BORDER-COLLAPSE: collapse; mso-yfti-tbllook: 1184; mso-padding-alt: 0in 5.4pt 0in 5.4pt" cellSpacing=0 cellPadding=0 width=277 border=0><TBODY><TR style="HEIGHT: 15.75pt; mso-yfti-irow: 0; mso-yfti-firstrow: yes"><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 48pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15.75pt; BACKGROUND-COLOR: transparent; mso-border-alt: solid windowtext .5pt" noWrap width=64>
#<o></o>

</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #f0f0f0; WIDTH: 79.9pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15.75pt; BACKGROUND-COLOR: transparent; mso-border-top-alt: solid windowtext .5pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt" noWrap width=107>
Combinations<o></o>

</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #f0f0f0; WIDTH: 79.75pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15.75pt; BACKGROUND-COLOR: transparent; mso-border-top-alt: solid windowtext .5pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt" noWrap width=106>
Mix<o></o>

</TD></TR><TR style="HEIGHT: 15pt; mso-yfti-irow: 1"><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 48pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt" noWrap width=64>
1<o></o>

</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #f0f0f0; WIDTH: 79.9pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt" noWrap width=107>
1,2,3,4<o></o>

</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; BACKGROUND: #c2d69a; PADDING-BOTTOM: 0in; BORDER-LEFT: #f0f0f0; WIDTH: 79.75pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt" noWrap width=106>
No combinations<o></o>

</TD></TR><TR style="HEIGHT: 15pt; mso-yfti-irow: 2"><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 48pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt" noWrap width=64>
2<o></o>

</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #f0f0f0; WIDTH: 79.9pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt" noWrap width=107>
1,234<o></o>

</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; BACKGROUND: #ffc000; PADDING-BOTTOM: 0in; BORDER-LEFT: #f0f0f0; WIDTH: 79.75pt; PADDING-TOP: 0in; BORDER-BOTTOM: #f0f0f0; HEIGHT: 15pt; mso-border-right-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt" width=106 rowSpan=4>
1-3 or 3-1<o></o>

</TD></TR><TR style="HEIGHT: 15pt; mso-yfti-irow: 3"><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 48pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt" noWrap width=64>
3<o></o>

</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #f0f0f0; WIDTH: 79.9pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt" noWrap width=107>
2,134<o></o>

</TD></TR><TR style="HEIGHT: 15pt; mso-yfti-irow: 4"><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 48pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt" noWrap width=64>
4<o></o>

</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #f0f0f0; WIDTH: 79.9pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt" noWrap width=107>
3,124<o></o>

</TD></TR><TR style="HEIGHT: 15.75pt; mso-yfti-irow: 5"><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 48pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15.75pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt" noWrap width=64>
5<o></o>

</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #f0f0f0; WIDTH: 79.9pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15.75pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt" noWrap width=107>
4,123<o></o>

</TD></TR><TR style="HEIGHT: 15pt; mso-yfti-irow: 6"><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 48pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt" noWrap width=64>
6<o></o>

</TD><TD style="BORDER-RIGHT: #f0f0f0; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #f0f0f0; WIDTH: 79.9pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt" noWrap width=107>
12,3,4<o></o>

</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; BACKGROUND: #00b0f0; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 79.75pt; PADDING-TOP: 0in; BORDER-BOTTOM: #f0f0f0; HEIGHT: 15pt" width=106 rowSpan=6>
2-1-1 only<o></o>

</TD></TR><TR style="HEIGHT: 15pt; mso-yfti-irow: 7"><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 48pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt" noWrap width=64>
7<o></o>

</TD><TD style="BORDER-RIGHT: #f0f0f0; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #f0f0f0; WIDTH: 79.9pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt" noWrap width=107>
13,2,4<o></o>

</TD></TR><TR style="HEIGHT: 15pt; mso-yfti-irow: 8"><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 48pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt" noWrap width=64>
8<o></o>

</TD><TD style="BORDER-RIGHT: #f0f0f0; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #f0f0f0; WIDTH: 79.9pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt" noWrap width=107>
14,2,3<o></o>

</TD></TR><TR style="HEIGHT: 15pt; mso-yfti-irow: 9"><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 48pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt" noWrap width=64>
9<o></o>

</TD><TD style="BORDER-RIGHT: #f0f0f0; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #f0f0f0; WIDTH: 79.9pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt" noWrap width=107>
23,1,4<o></o>

</TD></TR><TR style="HEIGHT: 15pt; mso-yfti-irow: 10"><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 48pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt" noWrap width=64>
10<o></o>

</TD><TD style="BORDER-RIGHT: #f0f0f0; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #f0f0f0; WIDTH: 79.9pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt" noWrap width=107>
24,1,3<o></o>

</TD></TR><TR style="HEIGHT: 15.75pt; mso-yfti-irow: 11"><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 48pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15.75pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt" noWrap width=64>
11<o></o>

</TD><TD style="BORDER-RIGHT: #f0f0f0; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #f0f0f0; WIDTH: 79.9pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15.75pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt" noWrap width=107>
34,1,2<o></o>

</TD></TR><TR style="HEIGHT: 15pt; mso-yfti-irow: 12"><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 48pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt" noWrap width=64>
12<o></o>

</TD><TD style="BORDER-RIGHT: #f0f0f0; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #f0f0f0; WIDTH: 79.9pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt" noWrap width=107>
12,34<o></o>

</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; BACKGROUND: #a5a5a5; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 79.75pt; PADDING-TOP: 0in; BORDER-BOTTOM: #f0f0f0; HEIGHT: 15pt" width=106 rowSpan=3>
2-2 only<o></o>

</TD></TR><TR style="HEIGHT: 15pt; mso-yfti-irow: 13"><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 48pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt" noWrap width=64>
13<o></o>

</TD><TD style="BORDER-RIGHT: #f0f0f0; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #f0f0f0; WIDTH: 79.9pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt" noWrap width=107>
13,24<o></o>

</TD></TR><TR style="HEIGHT: 15.75pt; mso-yfti-irow: 14"><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 48pt; PADDING-TOP: 0in; BORDER-BOTTOM: #f0f0f0; HEIGHT: 15.75pt; BACKGROUND-COLOR: transparent; mso-border-right-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt" noWrap width=64>
14<o></o>

</TD><TD style="BORDER-RIGHT: #f0f0f0; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #f0f0f0; WIDTH: 79.9pt; PADDING-TOP: 0in; BORDER-BOTTOM: #f0f0f0; HEIGHT: 15.75pt; BACKGROUND-COLOR: transparent" noWrap width=107>
14,23<o></o>

</TD></TR><TR style="HEIGHT: 15.75pt; mso-yfti-irow: 15; mso-yfti-lastrow: yes"><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 48pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15.75pt; BACKGROUND-COLOR: transparent; mso-border-alt: solid windowtext .5pt" vAlign=bottom noWrap width=64>
15<o></o>

</TD><TD style="BORDER-RIGHT: #f0f0f0; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #f0f0f0; WIDTH: 79.9pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15.75pt; BACKGROUND-COLOR: transparent; mso-border-top-alt: solid windowtext .5pt; mso-border-bottom-alt: solid windowtext .5pt" vAlign=bottom noWrap width=107>
1234<o></o>

</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; BACKGROUND: #00b050; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 79.75pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15.75pt" vAlign=bottom noWrap width=106>
All together<o></o>

</TD></TR></TBODY></TABLE>​
<o></o>
The above was done manually since the numbers are small, what about if I have 9 production lines or 20 production lines!!! ,,,,, How can I formulate this in Excel?

I want to enter any arbitrary number (i.e.4,7, 9, 10, 20 ….. etc.) and the program will give me all possible combinations.

Thanks in advance and I am really looking forward to hearing from you experts J

### Excel Facts

How to show all formulas in Excel?
Press Ctrl+` to show all formulas. Press it again to toggle back to numbers. The grave accent is often under the tilde on US keyboards.

#### diddi

##### Well-known Member
hi and welcome to the board

do you need the combinations or the number of combinations?

#### the_storm

##### New Member
Hi diddi

I need both of them.

Actually, I want to enter any arbitrary number of production lines (i.e.4,7, 9, 10, 20 ….. etc.) and the program will give me the number of possible combinations and will list all of these combinations as well.

Thanks and i am really hoping to find an answer for this issue.

#### shg

##### MrExcel MVP
If there are n items, then there are 2^n combinations including the null set. So you could generate a binary sequence and regard each 1 as denoting a member of the combination; e.g., for 4 items,

0000 ' none
1000 ' item 1 only
0100 ' item 2 only
1100 ' items 1 & 2
...
1110 ' items 1, 2, & 3
1111 ' items 1, 2, 3, & 4

#### the_storm

##### New Member

Hi shg4421,<?xml:namespace prefix = o ns = "urn:schemas-microsoft-comfficeffice" /><o></o>
<o></o>
Unfortunately you did not get my question. If you take a look to my first post you will see that the possible combinations for 3 items are 5 which is not 2^3 and the possible combinations for 4 items are 15 which is not 2^4.

I want to enter any arbitrary number of production lines (i.e.4,7, 9, 10, 20 ….. etc.) and the program will give me the number of possible combinations and will list all of these combinations as well in the same way given in the first post.

Thanks

<o></o>

#### shg

##### MrExcel MVP
Unfortunately, I still don't get your question.

It's not clear to me, for example, why 1, 2, 3, is not three combinations {1}, {2}, and {3}. That would make 7 combinations instead of 5, plus the empty set {}, which might not be of interest to you, but does round the combinations out to 2^3 = 8.

You're free to make your own definitions, but finding some common ground might be a path to a solution.

#### xenou

##### MrExcel MVP

As a product mix, 1 + (2,3) and 2 + (1,3) are indifferent. Both "product baskets" have the same three products in it no matter how you slice or dice it. So the logic isn't clear here.

Also, it doesn't help to include the Null or Empty set as no one will buy "nothing" from you at any price. Though it's a nice touch to include it to prove out the numbers of combinations mathematically.

#### tusharm

##### MrExcel MVP
What does the Combinations column represent?
So, with 3 production lines what does 1,2,3 mean? And the same question applies to 1,23?

How does each value in that column relate to the corresponding value in the Mix column?

Good day experts,

This is my first question in this forum and I am optimistic to find the perfect solution here in MrExcel J ….. My question is about formulating combinations.

Imagine that I have 3 different production lines (1, 2 & 3) and I want to find all the possible combination between those production lines to evaluate what is more economical combination. These combinations will vary from no combination to all together.

The solution of the three production lines (1,2 & 3) will be as follows:
<TABLE class=MsoNormalTable style="MARGIN: auto auto auto 4.65pt; WIDTH: 207.75pt; BORDER-COLLAPSE: collapse; mso-yfti-tbllook: 1184; mso-padding-alt: 0in 5.4pt 0in 5.4pt" cellSpacing=0 cellPadding=0 width=277 border=0><TBODY><TR style="HEIGHT: 16.5pt; mso-yfti-irow: 0; mso-yfti-firstrow: yes"><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 48pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 16.5pt; BACKGROUND-COLOR: transparent; mso-border-alt: solid windowtext .5pt" noWrap width=64>
#<?xml:namespace prefix = o ns = "urn:schemas-microsoft-comfficeffice" /><o></o>

</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #f0f0f0; WIDTH: 79.9pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 16.5pt; BACKGROUND-COLOR: transparent; mso-border-top-alt: solid windowtext .5pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt" noWrap width=107>
Combinations<o></o>

</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #f0f0f0; WIDTH: 79.85pt; PADDING-TOP: 0in; BORDER-BOTTOM: #f0f0f0; HEIGHT: 16.5pt; BACKGROUND-COLOR: transparent; mso-border-top-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt" noWrap width=106>
Mix<o></o>

</TD></TR><TR style="HEIGHT: 15.75pt; mso-yfti-irow: 1"><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 48pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15.75pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt" noWrap width=64>
1<o></o>

</TD><TD style="BORDER-RIGHT: #f0f0f0; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #f0f0f0; WIDTH: 79.9pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15.75pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt" noWrap width=107>
1,2,3<o></o>

</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; BACKGROUND: #c2d69a; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 79.85pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15.75pt" noWrap width=106>
No combinations<o></o>

</TD></TR><TR style="HEIGHT: 15pt; mso-yfti-irow: 2"><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 48pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt" noWrap width=64>
2<o></o>

</TD><TD style="BORDER-RIGHT: #f0f0f0; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #f0f0f0; WIDTH: 79.9pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt" noWrap width=107>
1,23<o></o>

</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; BACKGROUND: #ffc000; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 79.85pt; PADDING-TOP: 0in; BORDER-BOTTOM: black 1pt solid; HEIGHT: 15pt" width=106 rowSpan=3>
1-2 or 2-1<o></o>

</TD></TR><TR style="HEIGHT: 15pt; mso-yfti-irow: 3"><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 48pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt" noWrap width=64>
3<o></o>

</TD><TD style="BORDER-RIGHT: #f0f0f0; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #f0f0f0; WIDTH: 79.9pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt" noWrap width=107>
2,13<o></o>

</TD></TR><TR style="HEIGHT: 15.75pt; mso-yfti-irow: 4"><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 48pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15.75pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt" noWrap width=64>
4<o></o>

</TD><TD style="BORDER-RIGHT: #f0f0f0; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #f0f0f0; WIDTH: 79.9pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15.75pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt" noWrap width=107>
3,12<o></o>

</TD></TR><TR style="HEIGHT: 15.75pt; mso-yfti-irow: 5; mso-yfti-lastrow: yes"><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 48pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15.75pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt" noWrap width=64>
5<o></o>

</TD><TD style="BORDER-RIGHT: #f0f0f0; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #f0f0f0; WIDTH: 79.9pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15.75pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt" noWrap width=107>
123<o></o>

</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; BACKGROUND: #00b0f0; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 79.85pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15.75pt" width=106>
All together<o></o>

</TD></TR></TBODY></TABLE>​
<o></o>
If there is a 4 production lines (1,2,3 & 4) the solution will be as follows:
<TABLE class=MsoNormalTable style="MARGIN: auto auto auto 4.75pt; WIDTH: 207.65pt; BORDER-COLLAPSE: collapse; mso-yfti-tbllook: 1184; mso-padding-alt: 0in 5.4pt 0in 5.4pt" cellSpacing=0 cellPadding=0 width=277 border=0><TBODY><TR style="HEIGHT: 15.75pt; mso-yfti-irow: 0; mso-yfti-firstrow: yes"><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 48pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15.75pt; BACKGROUND-COLOR: transparent; mso-border-alt: solid windowtext .5pt" noWrap width=64>
#<o></o>

</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #f0f0f0; WIDTH: 79.9pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15.75pt; BACKGROUND-COLOR: transparent; mso-border-top-alt: solid windowtext .5pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt" noWrap width=107>
Combinations<o></o>

</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #f0f0f0; WIDTH: 79.75pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15.75pt; BACKGROUND-COLOR: transparent; mso-border-top-alt: solid windowtext .5pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt" noWrap width=106>
Mix<o></o>

</TD></TR><TR style="HEIGHT: 15pt; mso-yfti-irow: 1"><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 48pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt" noWrap width=64>
1<o></o>

</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #f0f0f0; WIDTH: 79.9pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt" noWrap width=107>
1,2,3,4<o></o>

</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; BACKGROUND: #c2d69a; PADDING-BOTTOM: 0in; BORDER-LEFT: #f0f0f0; WIDTH: 79.75pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt" noWrap width=106>
No combinations<o></o>

</TD></TR><TR style="HEIGHT: 15pt; mso-yfti-irow: 2"><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 48pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt" noWrap width=64>
2<o></o>

</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #f0f0f0; WIDTH: 79.9pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt" noWrap width=107>
1,234<o></o>

</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; BACKGROUND: #ffc000; PADDING-BOTTOM: 0in; BORDER-LEFT: #f0f0f0; WIDTH: 79.75pt; PADDING-TOP: 0in; BORDER-BOTTOM: #f0f0f0; HEIGHT: 15pt; mso-border-right-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt" width=106 rowSpan=4>
1-3 or 3-1<o></o>

</TD></TR><TR style="HEIGHT: 15pt; mso-yfti-irow: 3"><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 48pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt" noWrap width=64>
3<o></o>

</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #f0f0f0; WIDTH: 79.9pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt" noWrap width=107>
2,134<o></o>

</TD></TR><TR style="HEIGHT: 15pt; mso-yfti-irow: 4"><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 48pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt" noWrap width=64>
4<o></o>

</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #f0f0f0; WIDTH: 79.9pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt" noWrap width=107>
3,124<o></o>

</TD></TR><TR style="HEIGHT: 15.75pt; mso-yfti-irow: 5"><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 48pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15.75pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt" noWrap width=64>
5<o></o>

</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #f0f0f0; WIDTH: 79.9pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15.75pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt" noWrap width=107>
4,123<o></o>

</TD></TR><TR style="HEIGHT: 15pt; mso-yfti-irow: 6"><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 48pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt" noWrap width=64>
6<o></o>

</TD><TD style="BORDER-RIGHT: #f0f0f0; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #f0f0f0; WIDTH: 79.9pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt" noWrap width=107>
12,3,4<o></o>

</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; BACKGROUND: #00b0f0; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 79.75pt; PADDING-TOP: 0in; BORDER-BOTTOM: #f0f0f0; HEIGHT: 15pt" width=106 rowSpan=6>
2-1-1 only<o></o>

</TD></TR><TR style="HEIGHT: 15pt; mso-yfti-irow: 7"><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 48pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt" noWrap width=64>
7<o></o>

</TD><TD style="BORDER-RIGHT: #f0f0f0; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #f0f0f0; WIDTH: 79.9pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt" noWrap width=107>
13,2,4<o></o>

</TD></TR><TR style="HEIGHT: 15pt; mso-yfti-irow: 8"><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 48pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt" noWrap width=64>
8<o></o>

</TD><TD style="BORDER-RIGHT: #f0f0f0; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #f0f0f0; WIDTH: 79.9pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt" noWrap width=107>
14,2,3<o></o>

</TD></TR><TR style="HEIGHT: 15pt; mso-yfti-irow: 9"><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 48pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt" noWrap width=64>
9<o></o>

</TD><TD style="BORDER-RIGHT: #f0f0f0; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #f0f0f0; WIDTH: 79.9pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt" noWrap width=107>
23,1,4<o></o>

</TD></TR><TR style="HEIGHT: 15pt; mso-yfti-irow: 10"><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 48pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt" noWrap width=64>
10<o></o>

</TD><TD style="BORDER-RIGHT: #f0f0f0; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #f0f0f0; WIDTH: 79.9pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt" noWrap width=107>
24,1,3<o></o>

</TD></TR><TR style="HEIGHT: 15.75pt; mso-yfti-irow: 11"><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 48pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15.75pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt" noWrap width=64>
11<o></o>

</TD><TD style="BORDER-RIGHT: #f0f0f0; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #f0f0f0; WIDTH: 79.9pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15.75pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt" noWrap width=107>
34,1,2<o></o>

</TD></TR><TR style="HEIGHT: 15pt; mso-yfti-irow: 12"><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 48pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt" noWrap width=64>
12<o></o>

</TD><TD style="BORDER-RIGHT: #f0f0f0; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #f0f0f0; WIDTH: 79.9pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt" noWrap width=107>
12,34<o></o>

</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; BACKGROUND: #a5a5a5; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 79.75pt; PADDING-TOP: 0in; BORDER-BOTTOM: #f0f0f0; HEIGHT: 15pt" width=106 rowSpan=3>
2-2 only<o></o>

</TD></TR><TR style="HEIGHT: 15pt; mso-yfti-irow: 13"><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 48pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt" noWrap width=64>
13<o></o>

</TD><TD style="BORDER-RIGHT: #f0f0f0; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #f0f0f0; WIDTH: 79.9pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt" noWrap width=107>
13,24<o></o>

</TD></TR><TR style="HEIGHT: 15.75pt; mso-yfti-irow: 14"><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 48pt; PADDING-TOP: 0in; BORDER-BOTTOM: #f0f0f0; HEIGHT: 15.75pt; BACKGROUND-COLOR: transparent; mso-border-right-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt" noWrap width=64>
14<o></o>

</TD><TD style="BORDER-RIGHT: #f0f0f0; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #f0f0f0; WIDTH: 79.9pt; PADDING-TOP: 0in; BORDER-BOTTOM: #f0f0f0; HEIGHT: 15.75pt; BACKGROUND-COLOR: transparent" noWrap width=107>
14,23<o></o>

</TD></TR><TR style="HEIGHT: 15.75pt; mso-yfti-irow: 15; mso-yfti-lastrow: yes"><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 48pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15.75pt; BACKGROUND-COLOR: transparent; mso-border-alt: solid windowtext .5pt" vAlign=bottom noWrap width=64>
15<o></o>

</TD><TD style="BORDER-RIGHT: #f0f0f0; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #f0f0f0; WIDTH: 79.9pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15.75pt; BACKGROUND-COLOR: transparent; mso-border-top-alt: solid windowtext .5pt; mso-border-bottom-alt: solid windowtext .5pt" vAlign=bottom noWrap width=107>
1234<o></o>

</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; BACKGROUND: #00b050; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 79.75pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15.75pt" vAlign=bottom noWrap width=106>
All together<o></o>

</TD></TR></TBODY></TABLE>​
<o></o>
The above was done manually since the numbers are small, what about if I have 9 production lines or 20 production lines!!! ,,,,, How can I formulate this in Excel?

I want to enter any arbitrary number (i.e.4,7, 9, 10, 20 ….. etc.) and the program will give me all possible combinations.

Thanks in advance and I am really looking forward to hearing from you experts J

#### pgc01

##### MrExcel MVP
Hi

If I understand correctly you are using the term combination loosely and not in the mathematical sense, and what you want is the value of what in combinatorics is called a Bell number. A Bell number gives you the number of ways that a set can be divided in subsets.

There's a recursive formula that calculates the Bell numbers given the values of the previous ones. Try this udf:

Code:
``````Function Bell(n As Long) As Variant
Dim Bells As Variant
Dim j As Long, k As Long

ReDim Bells(0 To n)
Bells(0) = 1
Bells(1) = 1

For j = 2 To n
For k = 0 To j - 1
Bells(j) = Bells(j) + Application.Combin(j - 1, k) * Bells(k)
Next k
Next j
Bell = Bells(n)
End Function``````

Notice that the number grows very quickly and so if this is really what you wanted it doesn't give a practical result if you have more than a few production line. For ex., for 20 production lines you'd have to evaluate 51,724,158,235,372 different values.

Ex.:

In B1: =Bell(A1)

Remark: I am not validating the parameter of the function.

Last edited:

#### pgc01

##### MrExcel MVP
You can also generate the list just using formulas. In this case, however, you have to write the whole list because each value is calculated using the previous ones.

Ex.:

Enter the values in column A and in B1:B2

In B3:

=SUMPRODUCT(COMBIN(A3-1,\$A\$1:A2),\$B\$1:B2)

Copy down.

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