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

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(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:

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