The number of ways in which 6 boys and 5 girl | vedclass

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(C) To arrange $6$ boys and $5$ girls at a round table such that no two girls sit together,we first arrange the $6$ boys in a circle. The number of wa

Vedclass · Accepted Answer

$86400$

Vedclass · Answer

(C) To arrange $6$ boys and $5$ girls at a round table such that no two girls sit together,we first arrange the $6$ boys in a circle. The number of ways to arrange $6$ boys in a circle is $(6-1)! = 5! = 120$. After arranging the boys,there are $6$ gaps created between them. We need to place $5$ girls in these $6$ gaps such that no two girls are together. The number of ways to choose $5$ gaps out of $6$ is $^6C_5 = 6$. The number of ways to arrange the $5$ girls in the chosen gaps is $5! = 120$. Therefore,the total number of ways is $120 	imes 6 	imes 120 = 86400$.

The number of ways in which $6$ boys and $5$ girls can sit at a round table,if no two girls are to sit together,is

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