SOLUTION: find the number of ways to seat n married couples around a table in the following cases 1/ men and women are alternate 2/ every woman is next to her husband

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Question 331931: find the number of ways to seat n married couples around a table in the following cases
1/ men and women are alternate
2/ every woman is next to her husband
Answer by galactus(183) About Me  (Show Source):
You can put this solution on YOUR website!
Seat the n women around the table in (n-1)! ways. The n men are then seated in the n spaces between the women in n! ways.
Thus, there are n%21%28n-1%29%21 ways to seat the men and women alternating.
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Tie each married couple together and pretend they are one person.
We can seat them in (n-1)! ways. Now, since each couple can be switched around in 2 ways, there are 2^n ways to arrange all of them
So, there are %28n-1%29%21%2A2%5En ways to arrange the couples with the women sitting with their husbands.