Four boys and three girls stand in a queue fo | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(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?

Similar Questions

$2$ dice are thrown. Find the odds in favour of getting the sum $4$.

$2$ dice are thrown. Find the probability of getting a sum more than $7$.

There are two children in a family. The probability that both of them are boys is

$A$ box contains $10$ red balls and $15$ green balls. If two balls are drawn in succession,then the probability that one is red and the other is green is:

$A$ bag contains $4$ white,$5$ red,and $6$ blue balls. Three balls are drawn at random. What is the probability that all of them are red?

Vedclass Test Series

Exam Paper Generator

Online Exam Module