32. Suppose all n men at a party throw their hats in the center of the room....
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32. 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
2!
− 1 3!
+
1 4!
−+··· (−1)n n!
Note that as n → ∞ this converges to e−1. Is this surprising?
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