Abe and Zach live in Springfield. Suppose Abe's friends and Zach's friends are each a random sample of 50 out of the 1000 people who live in Springfield.
Find the probability mass function of them having $X$ mutual friends.
I figured the expected value is $(1000)(\frac{50}{1000})^2 = \frac{5}{2}$ since each person in Springfield has a $(\frac{50}{1000})^2$ chance of being friends with both Abe and Zach. However, how do I generalize this expected value idea to create a probability mass function that returns the probability of having $X$ mutual friends?