JEE Main · 2025 · 22 Jan 2025 · Shift 2 · Permutations and Combinations

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 :

Answer: (A)

Solution

Treat all girls as one block and all boys as one block; these two blocks can be arranged in

2!

ways, and the girls internally in

3!

ways.

For the boys, count arrangements of the 4 boys that keep

B_{1}

and

B_{2}

apart. Total arrangements of 4 boys:

4! = 24

. Arrangements with

B_{1}, B_{2}

adjacent: glue them into one unit, giving 3 units arranged in

3!

ways, times

2!

for the internal order of

B_{1}, B_{2}

3! \times 2! = 12

. So arrangements with

B_{1}, B_{2}

not adjacent:

24 - 12 = 12

.

Total arrangements:

2! \times 3! \times 12 = 2 \times 6 \times 12 = 144.

JEE Main · 2025 · 22 Jan 2025 · Shift 2 · Single correct option