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
 A: 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 $\frac{20\cdot 12}{2}=\boxed{120}.$
A: See you've got 5 men and 4 women. For the 1st pair you have 5 options for a man and for each 5 of the options for the man you have 4 options of choosing a women. That is
You can choose a man in 5 ways and for each corresponding way you have 4 ways to choose a women. So total options is 5*4=20
For the second pair ( now you are left with 4 men and 3 women )
You can choose a man in 4 ways and for each corresponding way you have 3 ways to choose a women. So total options is 4*3=12
For each 20 of the options of the 1st pair you have 12 options of the 2nd pair.
So total 20*12=240
But you could choose the second pair first and then choose the 1st one
 The thing is that you have counted it twice. 
So total options 240/2= 120
If you can't see why the division by 2 then reduce the number of people and manually form the pairs. You will see it.
