There is a theater. 5 men drop their hats to the cloakroom. What is the probability that each will get a different hat when they leave the theatre.

Is there a solution without using any formula?

There are 5!=120 cases.

We want a 1 to 1 function but 1 mustn't couple with 1.

12345-32154 This is one of the wanted cases. I can get 24 permutations like that.

so I got 24/120 but it is wrong.