MathCastle
ChallengeMediumInclusion–Exclusion, Derangements & Pigeonhole

Inclusion--Exclusion, Derangements & Pigeonhole · Medium problem

Six people check their hats, and the hats are returned at random, one to each person (a uniformly random permutation). Find the probability that exactly two people receive their own hat.

Express your answer as a common fraction.