Creating combinations where order IS important

[fboehlandt]

Hi everyone.
Upfront, apologies for the millionth question regarding permutations / combinations. I'm referring to this thread below about permutations and combinations:

http://www.mrexcel.com/forum/showthread.php?t=510330&highlight=permutation+ABC

I have noted that the suggested VBA code does not make provisions for cases where the order is important and the objective is to create combinations. For example, k = 2 out of n = 5 where the elements are A B C D E would yield:

AB
AC
AD
...
DE

In some instance, however, DE may not equal ED. Consequently, the combinations should end on ED. Does anybody have a suggestion or code snippet doing exactly that?

 

[GlennUK]

Is this always going to be 2 out of 5? Or are you going to want this to be any selection from any amount?

 

[fboehlandt]

I would like to allow for different selections and amounts. That is, within reason: the number of combinations (and permutations in particular) can quickly reach exorbitant sizes. I can probably make the changes myself using the original code. I was just wondering if anybody else has stumbled across this?
Essentially, there are four dimensions when 'drawing balls from and urn':
- order is relevant vs order is irrelevant (permutations vs combinations)
- replacement vs non-replacement
The existing code addresses the first dimension but not the second one (thus, my initial question got it exactly wrong). In the simplest example drawing 2 out of three elements A B C:

Combinations / no replacement:
AB
AC
BC

Permutations / no replacement:
AB
BA
AC
CA
BC
CB

Combinations / replacement:
AA
AB
AC
BB
BC
CC

Permutations / replacement:
AA
AB
AC
BA
BB
BC
CA
CB
CC

I need something that does all that for different selections and different amounts. Any help is greatly appreciated...

 

[fboehlandt]

p.s. of course it is feasible that k (as the number of elements drawn) is larger than n (the amount drawn from), as long as the balls are being replaced. So combinations like the following would be possible:

AAAA
AAAB
...
CCCC

But this isn't really the case with my specific problem.

 

[GTO]

You may like this: http://www.tushar-mehta.com/excel/tips/powerset.html

 

[fboehlandt]

Thanks Glenn,
that is a good starting point. The code is a bit messy but I can work from here. Also, it is missing option three aka combinations / replacement. I shall post again once I have the complete code. Thanks again

 

[GlennUK]

That was GTO, not me ( thanks GTO ). Am glad that you're getting somewhere with it.

 

[fboehlandt]

of course, mea culpa. Thanks to the both of you

 

[GTO]

Glad to be of what help I could be I find Tushar's articles very interesting and informative.