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 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?

Similar Questions

$A$ bag contains $21$ toys numbered $1$ to $21$. $A$ toy is drawn and then another toy is drawn without replacement. The probability that both toys will show even numbers is

Suppose $n \ge 3$ persons are sitting in a row. Two of them are selected at random. The probability that they are not together is

$A$ $5$-digit number is formed using the digits $1, 2, 3, 4, 5, 6,$ and $8$. What is the probability that the number has even digits at both ends?

Two cards are drawn at random from a pack of $52$ cards. The probability that both are the cards of spade is

From a class of $12$ girls and $18$ boys,two students are chosen randomly. What is the probability that both of them are girls?

Vedclass Test Series

Exam Paper Generator

Online Exam Module