The number of ways in which 5 male and 2 fema | vedclass

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(A) First,arrange the $5$ male members around a round table. The number of ways to arrange $n$ objects in a circle is $(n-1)!$. So,$5$ males can be se

Vedclass · Accepted Answer

$480$

Vedclass · Answer

(A) First,arrange the $5$ male members around a round table. The number of ways to arrange $n$ objects in a circle is $(n-1)!$. So,$5$ males can be seated in $(5-1)! = 4! = 24$ ways.After seating the $5$ males,there are $5$ gaps created between them.To ensure the $2$ females are not seated together,we must place them in these $5$ available gaps.The number of ways to choose and arrange $2$ females in $5$ gaps is given by the permutation formula ${}^5P_2 = \frac{5!}{(5-2)!} = 5 	imes 4 = 20$.Therefore,the total number of ways is $4! 	imes {}^5P_2 = 24 	imes 20 = 480$.

The number of ways in which $5$ male and $2$ female members of a committee can be seated around a round table so that the two female members are not seated together is:

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