By: Tao Steven Zheng (郑涛)

【Problem】

Suppose you and five of your friends each brought a hat to a party. The hats are then put into a large box for a random hat draw. What is the probability that nobody selects his or her own hat?

【Solution】

There are six people in total (you + five friends), so the number of possibilities that each person can get their hat is .

The number of possibilities that nobody selects their own hat is called the derangement problem. For six people, the number of derangements is:

The probability of each person get their wrong hat is:  

Therefore, the probability that nobody selects his or her own hat is 36.81%.