Consider the matching problem, Example 5m, and define An to be the number of ways in which...

Consider the matching problem, Example 5m, and define An to be the number of ways in which the N men can select their hats so that selects his own. Argue that

This formula, along with the boundary conditions A1 = 0, A2 = 1, can then be solved for AN,and the desired probability of no matches would be AN/N!