Combinatorics tennis match The prompt says, a tennis club has to select 2 mixed double pairs from a group of 5 men and 4 women. In how many ways can this be done?
There's total of 9 people and we need to choose of 8 people, that's what I think "2 mixed double pairs" means since one pair is 2 people and 2 double pairs would mean 2 * 4 = 8 people so I simply did 9 choose 8

The amount of ways to pick the first pair is simply 5*4=20.
The next one is simply 4*3=12. (You have to chose one man and one woman for each pair.)
But we've overcounted by two (the same pair of pairs situations), so it's $\frac{20\cdot 12}{2}=\boxed{120}.$
