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(D) First,arrange the $8$ men around a circular table. The number of ways to arrange $n$ objects in a circle is $(n-1)!$. So,the number of ways to arr

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$7! 	imes {}^{8}P_{4}$

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(D) First,arrange the $8$ men around a circular table. The number of ways to arrange $n$ objects in a circle is $(n-1)!$. So,the number of ways to arrange $8$ men is $(8-1)! = 7!$. This arrangement creates $8$ gaps between the men. To ensure no two women sit together,we must place the $4$ women in these $8$ gaps. The number of ways to choose and arrange $4$ women in $8$ gaps is given by the permutation formula ${}^{8}P_{4}$. Therefore,the total number of ways is $7! 	imes {}^{8}P_{4}$.

The number of ways of arranging $8$ men and $4$ women around a circular table such that no two women can sit together is

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