5 boys and 5 girls are sitting in a row rando | vedclass

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Question

(B) The total number of ways to arrange $10$ people ( $5$ boys and $5$ girls) in a row is $10!$.For the boys and girls to sit alternatively,there are

Vedclass · Accepted Answer

$1/126$

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(B) The total number of ways to arrange $10$ people ( $5$ boys and $5$ girls) in a row is $10!$.For the boys and girls to sit alternatively,there are two possible patterns:$1$. Boy,Girl,Boy,Girl,Boy,Girl,Boy,Girl,Boy,Girl$2$. Girl,Boy,Girl,Boy,Girl,Boy,Girl,Boy,Girl,BoyIn each pattern,the $5$ boys can be arranged in $5!$ ways and the $5$ girls can be arranged in $5!$ ways.Therefore,the number of favorable ways is $2 	imes (5! 	imes 5!)$.The probability is given by the ratio of favorable outcomes to total outcomes:$P = \frac{2 	imes 5! 	imes 5!}{10!}$$P = \frac{2 	imes 120 	imes 120}{3628800} = \frac{2 	imes 120}{10 	imes 9 	imes 8 	imes 7 	imes 6} = \frac{2}{30240} 	imes 120 = \frac{2}{252} = \frac{1}{126}$.

$5$ boys and $5$ girls are sitting in a row randomly. The probability that boys and girls sit alternatively is

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