*32. Suppose all men at a party throw their hats in the center of the room....

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*32. Suppose all ç men at a party throw their hats in the center of the room. Each man then randomly selects a hat. Show that the probability that none of the ç men winds up with his own hat is 1 1 1 (-1)"

+ + ... -——.

2! 3! 4! n\

Note that as ç -• oo this converges to e"1. Is this surprising? (Would you have incorrectly thought that this probability would go to 1 as ç -> oo?)

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