In how many ways can 5 boys and 5 girls sit i | vedclass

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Question

(B) To arrange $5$ boys and $5$ girls in a circle such that no two boys sit together,we first arrange the $5$ girls in a circle.The number of ways to

Vedclass · Accepted Answer

$4! 	imes 5!$

Vedclass · Answer

(B) To arrange $5$ boys and $5$ girls in a circle such that no two boys sit together,we first arrange the $5$ girls in a circle.The number of ways to arrange $n$ items in a circle is $(n-1)!$. Thus,$5$ girls can be arranged in $(5-1)! = 4!$ ways.After arranging the girls,there are $5$ gaps created between them. To ensure no two boys sit together,we must place the $5$ boys in these $5$ gaps.The number of ways to arrange $5$ boys in $5$ gaps is $5!$.Therefore,the total number of ways is $4! 	imes 5!$.

In how many ways can $5$ boys and $5$ girls sit in a circle so that no two boys sit together?

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