Combination and permutations

Question

A group contains n men and n women. How many ways are there to arrange these

people in a row if the men and women alternate?

Answer 1

The men can be arranged in n! ways. The women can be arranged in n! ways. These are independent so the total number of ways they can be arranged is (n!)(n!). But wait, you can start with a man in seat one or a woman in seat one. This doubles the result.

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