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

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(B) To seat $7$ men and $7$ women around a round table such that no two women sit together,we follow these steps:$1$. First,arrange the $7$ men around

Vedclass · Accepted Answer

$7! 	imes 6!$

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(B) To seat $7$ men and $7$ women around a round table such that no two women sit together,we follow these steps:$1$. First,arrange the $7$ men around the circular table. The number of ways to arrange $n$ distinct objects in a circle is $(n-1)!$. Thus,$7$ men can be seated in $(7-1)! = 6!$ ways.$2$. After seating the $7$ men,there are $7$ gaps created between them.$3$. To ensure no two women sit together,we must place the $7$ women in these $7$ gaps. The number of ways to arrange $7$ women in $7$ distinct gaps is $7!$.$4$. By the fundamental principle of counting,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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