# How many combinations??

##### New Member
Hello,

This may very well not be the place to post this question but I'm a writer not a math wiz and quite simply don't know how to figure this out.

I'm writing a newspaper article on hoarding and would like to determine how many different Christmas trees I can decorate using seven variables (different balls, bobbles and other embellishments) with a maximum grouping of two variables per tree/year.

For the sake of the calculation let's pretend there are equal amounts of each of the following items: Red satin balls; gold satin balls; red glitter icicles; gold glitter icicles; red mirrored snowflakes; gold mirrored snowflakes and red silk poinsettia bracts.

To avoid clutter—difficult for most hoarders I know—I'm limiting the combinations used each year to two. Sooo, one year I use red glitter icicles with gold mirrored snowflakes. . .the next year I use gold satin balls and red poinsettia bracts.

How many years can I decorate the same artificial tree without repeating the combinations? Is it even within the span of human life expectancy?

Thanks!!
Sheree

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#### shg

##### MrExcel MVP
=combin(7, 2) returns 21.

bc bd be bf bg
cd ce cf cg
de df dg
ef eg
fg

##### New Member

I looked at the Chinese Food Menu and was VERY intrigued but don't have the time now to sort it out (but will return someday). . .

Shg: Your formula "=combin(7,2) returns 21" was also interesting but I'm a bit rusty on which numbers/factors to plug in where. . .

BUT I did my own little diagram to see if I could come up with 21 and voila! It worked:

ab ac ad ae af ag
bc bd be bf bg
cd ce cf cg
de df dg
ef eg
fg

21!!

Is that the answer then? Seven different decorations....when used two at a time. . .will yield 21 different combinations?

Wow....if that's the answer then there's hope. . .I might live long enough to use all 21 combinations....

THANKS
Sheree

##### New Member
The alignment of my diagram above went wacky when I hit Post, thus explaining why it doesn't make sense now. In reality my columns were aligned properly...

##### Well-known Member
Is that the answer then? Seven different decorations....when used two at a time. . .will yield 21 different combinations?

shg said:

Using the menu program (yes I should have found the later version, thanks for posting it, I was wondering why the older one didn't have the macro I remembered):

Excel 2010
BCDEFGHIJK
2Cum:4971,1
3Cnt:771,2
5Inputs:111,4
6221,5
7331,6
8441,7
9552,2
10662,3
11772,4
122,5
132,6
14#2,7
151111,13,3
162121,23,4
173131,33,5
184141,43,6
195151,53,7
206161,64,4
217171,74,5
228211,24,6
239222,24,7
2410232,35,5
2511242,45,6
2612252,55,7
2713262,66,6
2814272,76,7
2915311,37,7
3016322,3
3117333,3
3218343,4
3319353,5
3420363,6
3521373,7
3622411,4
3723422,4
3824433,4
3925444,4
4026454,5
4127464,6
4228474,7
4329511,5
4430522,5
4531533,5
4632544,5
4733555,5
4834565,6
4935575,7
5036611,6
5137622,6
5238633,6
5339644,6
5440655,6
5541666,6
5642676,7
5743711,7
5844722,7
5945733,7
6046744,7
6147755,7
6248766,7
6349777,7
using Formulas
Cell Formulas
RangeFormula
C2=PRODUCT(relS:\$D\$3)
C3=COUNTA(Symbols)
C15=INDEX(Symbols, MOD(INT((Line - 1) * Cnt / Cum), Cnt) + 1)
B15=ROW()-ROW(B\$14)
D15=INDEX(Symbols, MOD(INT((Line - 1) * Cnt / Cum), Cnt) + 1)
F15=MIN(C15:D15)&","&MAX(C15:D15)
Named Ranges
NameRefers ToCells
'using Formulas'!Cnt='using Formulas'!B\$3
'using Formulas'!Cum='using Formulas'!B\$2
'using Formulas'!Line='using Formulas'!\$B2
'using Formulas'!relS='using Formulas'!B3
'using Formulas'!Symbols=INDEX('using Formulas'!B\$4:B\$14, 2):INDEX('using Formulas'!B\$4:B\$14, ROWS('using Formulas'!B\$4:B\$14) - 1)

(Paste to column K, remove duplicates and identical pairs)

#### Micron

##### Well-known Member
This all looks like a lot of work when you could just use the COMBIN function in Excel, right? It gives the answer 21.

##### Well-known Member
Yes but if you need the combinations instead of just the count.........

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