Suppose all n men at a party throw their hats in the center of the room. Each

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Suppose all n 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 n men selects his own hat is 1 21 11 + 3! 4! ...(-1)" n! Note that as no this converges to

e. Is this surprising?

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