My sister posed this question to me and I'm a little surprised to be struggling so much with it.
8 men and 8 women choose balls from a bin that contains 8 blue balls and 8 red balls. After the selection is done, what is the probability of that 4 men have a red ball and 4 men have a blue ball?
I was able to brute force the problem for 2 men, 2 women, 2 red and 2 blue balls (answer is 2/3) and I wrote a little script to brute force the answer for 4 men, 4 women, 4 red and 4 blue balls (answer is 20736 / 40320).
I can't figure out how to generalize the count though. Any help would be much appreciated.