A set of 200 people, consisting of 100 men and 100 women, is randomly divided into 100 pairs of 2 each. Give an upper bound to the probability that at most 30 of these pairs will consist of a man and a woman.

I intend to use the Chebyshev Inequality to solve it but it turns out that the prob. dist. for # of pairs consisting of a man and a woman is hard to find.

Anyone have any thought on it? Thanks a lot!