Of total N people, m people are good at mathematics and c people are good at computer science. What is the expected number of people good at both mathematics and computer science? Or what is the probability that r people are good at both mathematics and computer science. I have derived the formula. But it contains n!, p!, c! etc which is difficult to compute for large values (my real problem has large values for all of these). I am looking for a neat workable formula, I am hoping it exist since it is such a basic problem.