How many ways are there to arrange $n$ married couples in a line so that a husband and his wife are not together?

Asked Aug 18 '18 at 15:29

Active Aug 18 '18 at 19:05

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There are $2n$ people. There are $2n!$ ways to arrange them.

The number of ways to arrange them such that couples are always together is $n! \cdot 2^n$

How do you calculate the number of ways to arrange them such that no couples are together?

edited Aug 18 '18 at 16:19

inavda

asked Aug 18 '18 at 15:29

user585246

1

No, since it is possible that some couples are together while others are not. See Derangments – lulu Aug 18 '18 at 15:41

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