Five boys and five girls are to be seated aro | vedclass

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Question

(B) To seat $5$ boys and $5$ girls around a circular table such that no two boys and no two girls are together,they must sit in an alternating fashion

Vedclass · Accepted Answer

$2880$

Vedclass · Answer

(B) To seat $5$ boys and $5$ girls around a circular table such that no two boys and no two girls are together,they must sit in an alternating fashion ($B$-$G$-$B$-$G$-$B$-$G$-$B$-$G$-$B$-$G$).First,fix one boy at a position on the circular table. This can be done in $1$ way.The remaining $4$ boys can be arranged in the remaining $4$ seats in $(4-1)! = 3! = 6$ ways.There are $5$ gaps between the boys where the $5$ girls can be seated.The $5$ girls can be arranged in these $5$ gaps in $5! = 120$ ways.Therefore,the total number of ways is $1 	imes 6 	imes 120 = 720$.Wait,re-evaluating: The number of ways to arrange $n$ boys and $n$ girls in a circle such that they alternate is $(n-1)! 	imes n!$.For $n=5$,this is $(5-1)! 	imes 5! = 4! 	imes 5! = 24 	imes 120 = 2880$.Thus,the correct option is $B$.

Five boys and five girls are to be seated around a circular table. The number of ways in which they can be seated such that no two boys and no two girls are together is:

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