The teacher wants to arrange 5 students on the platform such that the boy $\mathrm{B}_1$ occupies second…

The teacher wants to arrange 5 students on the platform such that the boy $\mathrm{B}_1$ occupies second position and the girls $\mathrm{G}_1$ and $\mathrm{G}_2$ are always adjacent to each other, then the number of such arrangements is
  1. $24$
  2. $12$
  3. $8$
  4. $16$

Solution

There are 5 positions. Given that $\mathrm{B}_1$ occupies $2^{\text {nd }}$ position $\therefore \quad \mathrm{B}_1$ can be arranged in 1 way. As $G_1$ and $G_2$ are always together, none of them can take $1^{\text {st }}$ position. $\therefore \quad \mathrm{G}_1, \mathrm{G}_2$ and one of the remaining students can be arranged on $3^{\text {rd }}, 4^{\text {th }}$ and $5^{\text {th }}$ position when $\mathrm{G}_1$ and $\mathrm{G}_2$ are always together in $2 ! \times 2$ ! Ways. And remaining 2 students can be arranged in 2 ! Ways. $\therefore \quad$ The required number of arrangements $\begin{aligned} & =2 ! \times 2 ! \times 2 ! \\ & =8 \end{aligned}$

Asked in: MHT CET 2023 (11 May Shift 2)

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