Five boys and three girls are seated in a row | vedclass

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(C) Total number of ways to arrange $5$ boys and $3$ girls in a row is $n(S) = 8!$.To find the number of ways where all $3$ girls sit together,we trea

Vedclass · Accepted Answer

$3/28$

Vedclass · Answer

(C) Total number of ways to arrange $5$ boys and $3$ girls in a row is $n(S) = 8!$.To find the number of ways where all $3$ girls sit together,we treat the $3$ girls as a single unit. Now,we have $5$ boys and $1$ unit of girls,totaling $6$ entities.These $6$ entities can be arranged in $6!$ ways,and the $3$ girls within their unit can be arranged in $3!$ ways.So,$n(E) = 6! 	imes 3!$.The required probability is $P(E) = \frac{n(E)}{n(S)} = \frac{6! 	imes 3!}{8!} = \frac{6! 	imes 6}{8 	imes 7 	imes 6!} = \frac{6}{56} = \frac{3}{28}$.

Five boys and three girls are seated in a row at random. What is the probability that all three girls sit together?

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