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# In how many ways can 5 men and 5 women be seated in a

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Intern
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In how many ways can 5 men and 5 women be seated in a [#permalink]  02 Jun 2005, 09:58
In how many ways can 5 men and 5 women be seated in a circular table so that no two men or two women can be seated next to each other?

Thanks
Senior Manager
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Re: Perm and Comb [#permalink]  02 Jun 2005, 10:38
A circular permutation to seat 5 men in a circle = 4!.
In between the 5 spaces, 5 women can be distributed in 5! ways.
Total = 4!x5!
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Manager
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could somebody please explain the logic behind (5-1)! for circular arrangements? i know that's the rule, but there are still 5 men and 5 women sitting at the table. why don't we have to account for one?
Director
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july05 wrote:
could somebody please explain the logic behind (5-1)! for circular arrangements? i know that's the rule, but there are still 5 men and 5 women sitting at the table. why don't we have to account for one?

you need 1 person to serve as a point of reference, and then arrange the rest around that person.
Manager
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makes sense. thanks a lot.
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