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(B) Total number of ways to arrange $4$ boys and $3$ girls in a queue is $7!$.For them to be in alternate positions,the arrangement must be $B G B G B

Vedclass · Accepted Answer

$\frac{1}{35}$

Vedclass · Answer

(B) Total number of ways to arrange $4$ boys and $3$ girls in a queue is $7!$.For them to be in alternate positions,the arrangement must be $B G B G B G B$.Number of ways to arrange $4$ boys in the $4$ designated positions is $4!$.Number of ways to arrange $3$ girls in the $3$ designated positions is $3!$.Favourable cases $= 4! 	imes 3!$.Required probability $= \frac{4! 	imes 3!}{7!} = \frac{24 	imes 6}{5040} = \frac{144}{5040} = \frac{1}{35}$.

Four boys and three girls stand in a queue for an interview. What is the probability that they will be in alternate positions?

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