Consider the matching problem, Example 5m, and define A N to be the number of ways in
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Consider the matching problem, Example 5m, and define AN 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 A1 = 0, A2 = 1, can then be solved for AN, and the desired probability of no matches would be AN/N!.
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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 the full answer
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