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# Statistics - how many different ways to make n?

Please teach me step by step how to do the following questions. I'm stuck

1. Suppose we have a group of n women and n men, all heterosexual and all strictly monogamous. How many ways are there to make n couples out of these 2n people? 2. Suppose we have 2n people, each of whom is bisexual but strictly monogamous. How many ways are there to make n couples out of these 2n people?

### 1 Answer

- stanschimLv 74 weeks agoFavorite Answer
1. There should be n! couples possible. Once the first man is paired with any of the n women, then there are only (n-1) women available for the second man. Once the first and second men have been paired, then there are only (n-2) women available for the third, and so on. Using the counting principle, we would multiply all possibilities for each pairing.

2. We could think of counting for the second problem as (2nC2); taking all combinations of 2n people, two at a time. This is the same as (2n!) / [(2!)(2n-2)!].

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