In a group of 3 girls and 4 boys,there are tw | vedclass

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

Question

(A) Step $1$: Treat the group of $3$ girls as one unit and the group of $4$ boys as one unit. The number of ways to arrange these $2$ units is $2! = 2

Vedclass · Accepted Answer

$144$

Vedclass · Answer

(A) Step $1$: Treat the group of $3$ girls as one unit and the group of $4$ boys as one unit. The number of ways to arrange these $2$ units is $2! = 2$.Step $2$: Within the girls' unit,the $3$ girls can be arranged in $3! = 6$ ways.Step $3$: Within the boys' unit,the $4$ boys can be arranged in $4! = 24$ ways. Total arrangements with all girls together and all boys together is $2 	imes 6 	imes 24 = 288$.Step $4$: Now,calculate the arrangements where $B_1$ and $B_2$ are adjacent. Treat $(B_1, B_2)$ as one unit. The $4$ boys can be arranged in $3! 	imes 2! = 12$ ways. Total arrangements with girls together,boys together,and $B_1, B_2$ adjacent is $2 	imes 6 	imes 12 = 144$.Step $5$: The number of ways where $B_1$ and $B_2$ are not adjacent is $288 - 144 = 144$.

In a group of $3$ girls and $4$ boys,there are two boys $B_1$ and $B_2$. The number of ways in which these girls and boys can stand in a queue such that all the girls stand together,all the boys stand together,but $B_1$ and $B_2$ are not adjacent to each other,is:

Similar Questions

Let $m$ and $n$ $(m < n)$ be two $2$-digit numbers. Then the total number of pairs $(m, n)$ such that $\operatorname{gcd}(m, n) = 6$ is . . . . . . .

$^{37}C_4 + \sum_{r=1}^{5} {^{(42-r)}C_r} = $

The number of all possible combinations of $4$ letters which are taken from the letters of the word $ACCOMMODATION$ is

$9$ balls are to be placed in $9$ boxes. $3$ boxes are so small that they cannot hold $5$ balls. In how many ways can one ball be placed in each box?

Ten students are seated at random in a row. The probability that two particular students are not seated side by side is

Vedclass Test Series

Exam Paper Generator

Online Exam Module