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 winds up with his own hat is 1/2! – 1/3! + 1/4! - + …. (-1)n/n!. Note that as this converges to e-1. Is this surprising ? (would you have incorrectly thought that this probability would go to 1 as ?)