## Hats

Here’s a fun math problem…

Suppose there are *n* people. Each person has a hat.

Now, you collect all the hats, and distribute them back randomly. There is a certain probability that *no one* will get their own back.

What is the limit of this probability as *n* approaches infinity?

*Hint:* It’s a probability, so it’ll be in the [0,1] range.

(I’ll post a solution in a few days.)