# Derangements: Everything about them and More! (ESSAY)

Here’s a twist on a classic puzzle:

*Twenty men check their hats into a cloak room. But the cloak boy is somewhat disorganized and forgets which hats belong to whom and so, at the end of the evening, decides to hand hats back to the gentlemen at random. Ten of the men are lawyers. What is the probability that no lawyer gets his own hat back?*

In this essay we talk about everything you could possibly want to know about derangements and “sub-derangements” ( a new term invented for this puzzle!)