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

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(A) To arrange $5$ males and $2$ females around a round table such that the $2$ females are not together,we use the gap method.First,arrange the $5$ m

Vedclass · Accepted Answer

$480$

Vedclass · Answer

(A) To arrange $5$ males and $2$ females around a round table such that the $2$ females are not together,we use the gap method.First,arrange the $5$ males around the circular table. The number of ways to arrange $n$ objects in a circle is $(n-1)!$. Thus,$5$ males can be seated in $(5-1)! = 4! = 24$ ways.After seating the $5$ males,there are $5$ gaps created between them.We need to place the $2$ females in these $5$ gaps so that no two females are adjacent. The number of ways to choose and arrange $2$ females in $5$ gaps is given by the permutation formula ${}^5P_2$.${}^5P_2 = \frac{5!}{(5-2)!} = 5 	imes 4 = 20$.Therefore,the total number of ways is $24 	imes 20 = 480$.

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 are not seated together is

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