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

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

Vedclass · Accepted Answer

$6! 	imes 5!$

Vedclass · Answer

(A) First,arrange the $6$ men at a round table. The number of ways to arrange $n$ objects in a circle is $(n-1)!$. So,$6$ men can be arranged in $(6-1)! = 5!$ ways.After arranging the men,there are $6$ gaps created between them.Since no two women should sit together,we need to place $5$ women in these $6$ gaps.The number of ways to choose $5$ gaps out of $6$ is $^6C_5$,and the $5$ women can be arranged in these gaps in $5!$ ways.Alternatively,we can place $5$ women in $6$ gaps in $P(6, 5)$ ways.Total number of ways $= 5! 	imes P(6, 5) = 5! 	imes \frac{6!}{(6-5)!} = 5! 	imes 6!$.

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 given by

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