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# Free math help message board?

Original post made by rusty at math on Jul 14, 2008

I was trying to explain to my daughter about how you can calculate the number of different pairings of objects you could make if you know the total number of objects in a group, but have forgotten the forumula. I can do it by manually calculating it, but I've forgotten the expression/equation and I'd like to post the question and have someone help us out.

Say we have six objects: a b c d e & f

I know that if I pair them together ab, ac, ad, etc. the total number of possible combinations is 15. If there are only five objects there are nine possible combinations, and if there are four objects there are six possible combinations, etc.

I can't even remember the name of this type of problem or what branch of mathematics this is in order to look it up on Wikipedia. Is this algebra or probability?

I'd love to find a free resource for posting these kinds of questions in the future.

Comments (3)

on Jul 14, 2008 at 5:33 pm

The keyword is Combinatorial Analysis. This link may help: Web Link

on Jul 14, 2008 at 6:47 pm

If you have N objects, the number of possible pairings is (N*(N-1))/2.

Explanation: you have a choice of N objects for the first element of the pairing. Then you have a choice of N-1 objects for the second element. This yields N*(N-1) combinations. But each possible pairing will be generated twice this way (eg, as AB and as BA) so you have to divide by two.

So, the number of possible pairings of 6 elements is (6*5)/2 = 15.

on Jul 14, 2008 at 9:57 pm

Thanks very much!

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