The number of ways in which 6 men and 5 women | vedclass

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(A) First,arrange the $6$ men around a round table. The number of ways to arrange $n$ objects in a circle is $(n-1)!$. So,$6$ men can be seated in $(6

Vedclass · Accepted Answer

$6! 	imes 5!$

Vedclass · Answer

(A) First,arrange the $6$ men around a round table. The number of ways to arrange $n$ objects in a circle is $(n-1)!$. So,$6$ men can be seated in $(6-1)! = 5!$ ways.There are $6$ gaps created between the $6$ men where the $5$ women can be seated so that no two women sit together.The number of ways to arrange $5$ women in these $6$ gaps is given by the permutation formula $P(6, 5) = \frac{6!}{(6-5)!} = 6!$.Therefore,the total number of ways is $5! 	imes 6!$.

The number of ways in which $6$ men and $5$ women can dine at a round table,if no two women are to sit together,is:

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