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A football team consists of 20 offensive and 20 defensive players. The players are to be...

A football team consists of 20 offensive and 20 defensive players. The players are to be paired in groups of 2 for the purpose of determining roommates. If the pairing is done at random, (1) how many ways are there to divide the 40 players into unordered pairs of 2 each? (2) what is the probability that there are exactly 6 offensive-offensive roommate pairs?

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