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 arrangements where all $6$ girls sit together,we tr

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 arrangements where all $6$ girls sit together,we treat the $6$ girls as a single unit. This unit along with the $6$ boys gives us $7$ entities,which can be arranged in $7!$ ways.The $6$ girls within their unit can be arranged among themselves in $6!$ ways.So,the number of favorable arrangements is $7! 	imes 6!$.The required probability is $\frac{7! 	imes 6!}{12!} = \frac{7! 	imes 720}{12 	imes 11 	imes 10 	imes 9 	imes 8 	imes 7!} = \frac{720}{95040} = \frac{1}{132}$.

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

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