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

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Question

(A) Total number of ways to arrange $12$ people in a row is $n = 12!$.For the boys and girls to sit alternatively,there are two possible patterns:$1$.

Vedclass · Accepted Answer

$\frac{1}{462}$

Vedclass · Answer

(A) Total number of ways to arrange $12$ people in a row is $n = 12!$.For the boys and girls to sit alternatively,there are two possible patterns:$1$. Boy-Girl-Boy-Girl-Boy-Girl-Boy-Girl-Boy-Girl-Boy-Girl$2$. Girl-Boy-Girl-Boy-Girl-Boy-Girl-Boy-Girl-Boy-Girl-BoyIn each pattern,the $6$ boys can be arranged in $6!$ ways and the $6$ girls can be arranged in $6!$ ways.Thus,the total number of favourable ways is $m = 6! 	imes 6! + 6! 	imes 6! = 2 	imes (6! 	imes 6!)$.The required probability is $P = \frac{m}{n} = \frac{2 	imes 6! 	imes 6!}{12!}$.Calculating the value: $P = \frac{2 	imes 720 	imes 720}{479001600} = \frac{1036800}{479001600} = \frac{1}{462}$.

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

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