In how many ways can 7 men and 7 women be sea | vedclass

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Question

(B) To seat $7$ men and $7$ women around a round table such that no two women sit together,we first arrange the $7$ men around the table.The number of

Vedclass · Accepted Answer

$7! 	imes 6!$

Vedclass · Answer

(B) To seat $7$ men and $7$ women around a round table such that no two women sit together,we first arrange the $7$ men around the table.The number of ways to arrange $7$ men in a circle is $(7-1)! = 6!$.This arrangement creates $7$ gaps between the men.Since no two women can sit together,we must place the $7$ women in these $7$ gaps.The number of ways to arrange $7$ women in $7$ gaps is $7!$.Therefore,the total number of ways is $6! 	imes 7!$.

In how many ways can $7$ men and $7$ women be seated around a round table such that no two women sit together?

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