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

$$

\frac{1}{2!} - \frac{1}{3!} + \frac{1}{4!} + ... + \frac{(-1)^n}{n!}

$$

Note that as *n* → ∞ this converges to *e*^-1. Is this surprising?