Six boys and six girls sit in a row randomly. | vedclass

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(B) Total number of ways to arrange $6$ boys and $6$ girls in a row is $12!$.To find the number of ways where all $6$ girls sit together,we treat the

Vedclass · Accepted Answer

$\frac{1}{132}$

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(B) Total number of ways to arrange $6$ boys and $6$ girls in a row is $12!$.To find the number of ways where all $6$ girls sit together,we treat the $6$ girls as a single unit. Now,we have $6$ boys and $1$ unit of girls,totaling $7$ entities,which can be arranged in $7!$ ways.Within the unit,the $6$ girls can be arranged among themselves in $6!$ ways.Thus,the number of favorable arrangements is $7! 	imes 6!$.The required probability is $\frac{7! 	imes 6!}{12!} = \frac{7! 	imes 6 	imes 5 	imes 4 	imes 3 	imes 2 	imes 1}{12 	imes 11 	imes 10 	imes 9 	imes 8 	imes 7!} = \frac{720}{95040} = \frac{1}{132}$.

Six boys and six girls sit in a row randomly. What is the probability that the six girls sit together?

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