Choosing given number of items from different subsets

Question

A gathering is attended by A women and B men.

Women individually, independently of each other, have a p probability of getting to know each other, while men's chance of getting to know each other is also p.

What is the probability that by selecting a man and a woman, the two of them met exactly x persons?

 Women and men cannot get to know each other.

Answer 1

Together, they had the chance of meeting A+B-2 people, each with probability p. Thus, the probability of meeting x people is

C(A+B-2, x)p^x(1-p)^A+B-2-x