Fifty pairs of individuals playing in a bridge tournament have been seeded 1,, 50. In the first part of the tournament, the 50 are randomly divided into 25 east-west pairs and 25 north-south pairs.

(a) What is the probability that x of the top 25 pairs end up playing east-west?

(b) What is the probability that all of the top five pairs end up playing the same direction?

(c) If there are 2n pairs, what is the pmf of X = the number among the top n pairs who end up playing east-west? What are E(X) and V(X)?