event that no matches occurs. Denote
event that the first man selects his own hat.
Identify the boundary conditions.
Prove by induction.
Now what is the compliment?
The Problem " Suppose that each man at a party throws his hat into the center of the room. The hats are first mixed up and then randomly selected. Whats the probability that exactly k of men select their own hats?"
The final Solution is (1-1+1/2!-1/3!+...+(-1)^n-k/(N-k)!)/k!
I know that the solution can be found by computing the complement of the probability of none of the men getting the matching hat, but it is not working. Why?