quasi
Posts:
12,067
Registered:
7/15/05


Re: how many ways to pick two teams of 10 out of a group of 20 people
Posted:
Feb 5, 2013 3:46 AM


G Patel wrote:
>Is it 20 choose 10 or do I have to divide by 2?
You have to divide by 2.
Let S be a set of 20 people. There are (20choose10) 10person subsets of S, and for each such choice, we can create the teams A,B where A is the chosen subset and B is the complement of A. But B is also one of the possible choices for a 10person subset of S, and had B been the chosen subset, the teams would also be A,B. Thus, the correspondence between the set of 10person subsets of S and unordered pairs A,B of 10person teams is a 2to1 correspondence. Therefore the number of ways to pick two 10person teams from 20 people is (20choose10)/2.
quasi

