8 friends are playing a tennis game together. How many different doubles games of tennis can they play?
The Attempt at a Solution
Well, I solved this problem by saying: we choose a group 4 people from 8 to play, so order is not important, this is C(8,4). If those 4 people are A,B,C,D, they can play together in 3 different ways: AB/CD; AC/BD; AD/BC, so the solution is: 3C(8,4) = 210.
I tried doing this in another way, but I suppose I am doublecounting something. This was my approach:
For one team, we choose 2 people out of 8. For the other team, we choose 2 people out of 6 (since 2 out of 8 players are already taken). So, the answer would be: C(8,2)*C(6,2). Now, I am pretty sure that I have doublecounted, but I don't know exactly what it is I have doublecounted.
It would be great of someone could help me!