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A football team consists of 20 black and 20 white players. The players are to be paired in groups of 2 for the purpose of determining roommates.

a) If the pairing is done at random, what is the probability that there are no white-black roommate pairs?

b) What is the probability that there are 2i white-black roommate pairs, i = 1, 2, ..., 10?

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