Consider the matching problem, Example 5m, and define A N to be the number of ways in which the men can select their hats so that no man selects his own Argue that This formula, along with the boundary conditions A 1 0, A 2 1, can then be solved for A N , and the desired probability of no matches would be A N N AN (N 1)(AN 1 AN 2)

Question: Consider the matching problem, Example 5m, and define A N to be the number of ways in which the men can select their hats so

Consider the matching problem, Example 5m, and define A_N to be the number of ways in which the men can select their hats so that no man selects his own. Argue that

AN = (N 1)(AN-1+ AN-2)

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

AN = (N 1)(AN-1+ AN-2)

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The formula AN N1AN1AN2 follows from the principle of inclusionexclusion Lets consider the number of ways the men can select their hats such that at l... View full answer

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