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 :

Question

Dr. Abubacker · Accepted Answer

[Solution by Dr. Abubacker] Treat the girls as one block and the boys as one block: $2!$ orders of the blocks, $3!$ arrangements of the girls. Boys: $4!-2\cdot3!=24-12=12$ arrangements with $B_1,B_2$ not adjacent. Total $=2\cdot6\cdot12=144$. Answer (2).

Q. 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 :

Explanation

Reviewed by Dr. Abubacker

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