In how many ways can 5 boys and 5 girls be se | vedclass

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(B) First,arrange the $5$ boys around a circular table. The number of ways to arrange $n$ distinct objects in a circle is $(n-1)!$. So,$5$ boys can be

Vedclass · Accepted Answer

$5! 	imes 4!$

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(B) First,arrange the $5$ boys around a circular table. The number of ways to arrange $n$ distinct objects in a circle is $(n-1)!$. So,$5$ boys can be seated in $(5-1)! = 4!$ ways.After seating the boys,there are $5$ gaps created between them.To ensure no two girls sit together,we must place the $5$ girls in these $5$ gaps. The number of ways to arrange $5$ girls in $5$ gaps is $5!$ ways.Therefore,the total number of ways is $4! 	imes 5!$.

In how many ways can $5$ boys and $5$ girls be seated around a circular table such that no two girls are together?

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