If seven women and seven men are to be seated | vedclass

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Question

(A) To ensure that there is a man on either side of every woman,the men and women must alternate around the circular table.First,we arrange the $7$ me

Vedclass · Accepted Answer

$6! 7!$

Vedclass · Answer

(A) To ensure that there is a man on either side of every woman,the men and women must alternate around the circular table.First,we arrange the $7$ men around the circular table. The number of ways to arrange $n$ items in a circle is $(n-1)!$. Thus,$7$ men can be seated in $(7-1)! = 6!$ ways.Once the men are seated,there are $7$ distinct gaps created between them.Since every woman must have a man on either side,we must place the $7$ women into these $7$ gaps.The number of ways to arrange $7$ women in these $7$ gaps is $7!$.Therefore,the total number of seating arrangements is $6! 	imes 7!$.

If seven women and seven men are to be seated around a circular table such that there is a man on either side of every woman,then the number of seating arrangements is

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