# Website that will create combinations?

February 12, 2007 6:01 AM Subscribe

I'm working on a presentation for a public speaking class, and my chosen topic is group choice. Is there a website (or program) that I could use to generate all possible preference orderings for a specific set of preferences?

Or just numbers in general? It's not central to my presentation, but I'd like to have a slide or two that I could use to demonstrate how many different sets of individual preferences are possible given a certain number of alternatives, in order to explain why group choice is such a difficult and interesting topic. Moreover, I'd rather not go through and do all of the preference orderings/rankings by hand...

Or just numbers in general? It's not central to my presentation, but I'd like to have a slide or two that I could use to demonstrate how many different sets of individual preferences are possible given a certain number of alternatives, in order to explain why group choice is such a difficult and interesting topic. Moreover, I'd rather not go through and do all of the preference orderings/rankings by hand...

If you're asking, how many different ways can I arrange a set of

Factorials become very large very quickly, so showing all possible combinations might be excessive. For example, 10! is 3,628,800.

posted by Khalad at 7:48 AM on February 12, 2007

*n*items, the answer is*n*!. So if, for example, you were asked to rank five items from 1 to 5 in order of preference, there would be 5! = 5×4×3×2×1 = 120 ways you could rank those items.Factorials become very large very quickly, so showing all possible combinations might be excessive. For example, 10! is 3,628,800.

posted by Khalad at 7:48 AM on February 12, 2007

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If order is important, having 5 people choose 10 things leads to 5

^{10}different combinations, or 9,765,625.This sounds suspiciously similar to what Davar was trying to do in a previous question.

posted by demiurge at 6:13 AM on February 12, 2007