In the first part of the tourna- ment, the 20 are randomly divided into 10 east-west pairs

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In the first part of the tourna- ment, 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 X = the number among the top n pairs who end up playing east-west? What are E(X) and V(X)?

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