In the first part of the tournament, the 20 are randomly divided into 10 east–west pairs and 10 north–south pairs.

a. What is the probability that x of the top 10 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 among the top n pairs who end up playing east–west?

What are E(X) and V(X)?