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(B) Total number of people $= 4 	ext{ boys} + 3 	ext{ girls} = 7 	ext{ people}$.Total ways to arrange $7$ people in a queue $= 7!$.For the boys and

Vedclass · Accepted Answer

$\frac{1}{35}$

Vedclass · Answer

(B) Total number of people $= 4 	ext{ boys} + 3 	ext{ girls} = 7 	ext{ people}$.Total ways to arrange $7$ people in a queue $= 7!$.For the boys and girls to stand 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 $= 4!$.Number of ways to arrange $3$ girls in the $3$ designated positions $= 3!$.Total favourable arrangements $= 4! 	imes 3!$.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 stand in alternate positions?

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