In how many ways can 6 men and 5 women be sea | vedclass

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

Vedclass · Accepted Answer

$5! 	imes P(6, 5)$

Vedclass · Answer

(C) First,arrange the $6$ men around a circular 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.This arrangement creates $6$ gaps between the men where the $5$ women can be seated.To ensure no two women sit together,we choose $5$ gaps out of $6$ and arrange the $5$ women in them. This can be done in $P(6, 5)$ ways.Total number of ways $= 5! 	imes P(6, 5) = 120 	imes 720 = 86400$.

In how many ways can $6$ men and $5$ women be seated around a circular table if no two women are to be seated together?

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