Basic statistics question

I was about to choose some characters for a computer game when I began to wonder : how many combinations (order isn’t important, I mean [a,b,c,d] is the same combination than [c,a,d,b]) of 4 different elements (characters, in this case) in a set of 14 are there? What formula should I apply? I learnt that at some point in the past, but I can’t figure it out now…

14!/(4!)(10!)=1001 different combinations

Thanks a lot!
But could someone explain me (roughly) the logic behind this formula? Not that I really need to know ( I didn’t need to know the formula, either), but I’m curious…I suppose 14! is the total number of possible combinations of 5 different ordered elements (don’t know wheter “ordered” is the correct word in english or not…I hope younunderstand what I mean), but why should I divide it by 4! times 10! when I’m not concerned about order?
So, if someone has too much time in his/her hands, and doesn’t mind answering…

Your OP asks for how many different 4 number sets you can get from a set of size 14. Your follow up mentions 5, not 4. If you want 5 then it would be:

14!/(5!)(9!)=2002 different combinations.

I don’t want to get into the ‘philosophy’ of Combinations but the formula is:

nCr=n!/((r!)(n-r)!)

If order is not important (permutations) then the formula is:

nPr=n!/(n-r)!

Oops, permutation=if order is important

14! is the number of ways to arrange 14 different objects.

Imagine seeing all 14 objects in a row. You only care about the first 4 of them. The arrangement of the last 10 doesn’t matter.
There are 10! ways to arrange them. So you divide by 10! to get 14!/10!

This is now the number of ways to take 4 objects from 14 where you care about the order.

There are 4! ways to arrange 4 objects, so now you divide by 4! to get 14!/ (10! * 4!)

This is now the number of ways to take 4 objects from 14 where you don’t care about the order.

I hope this helps.

Ed

Also, you need to divide by r! for combinations because, if you have a 4 member set, there are 4! combinations where they have the same members but different order. That’s why, if order is not important, that you divide by r!.

Thanks to you both…It’s perfectly clear, now!

I’ll be able to play my computer game with my mind in peace (at least as long as I won’t wonder about the likehood of my character being killed by a +2 arrow while wearing an armor class 5 studded leather :wink: )