The teacher wants to arrange 5 students on th | vedclass

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(C) There are $5$ positions in total. The boy $B_1$ is fixed at the $2^{	ext{nd}}$ position.Remaining positions are $1^{	ext{st}}, 3^{	ext{rd}}, 4^

Vedclass · Accepted Answer

$8$

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(C) There are $5$ positions in total. The boy $B_1$ is fixed at the $2^{	ext{nd}}$ position.Remaining positions are $1^{	ext{st}}, 3^{	ext{rd}}, 4^{	ext{th}}, 5^{	ext{th}}$.Let the $5$ students be $B_1, G_1, G_2, S_1, S_2$.Since $G_1$ and $G_2$ must be adjacent,we treat them as a single unit $(G_1G_2)$.Now we have the units: $(G_1G_2), S_1, S_2$ to be placed in the remaining $4$ positions,such that $B_1$ is at the $2^{	ext{nd}}$ position.Case $1$: $(G_1G_2)$ occupies positions $(3, 4)$.Remaining positions $1$ and $5$ are filled by $S_1, S_2$ in $2!$ ways. $G_1, G_2$ can be arranged in $2!$ ways.Number of ways $= 2! 	imes 2! = 4$.Case $2$: $(G_1G_2)$ occupies positions $(4, 5)$.Remaining positions $1$ and $3$ are filled by $S_1, S_2$ in $2!$ ways. $G_1, G_2$ can be arranged in $2!$ ways.Number of ways $= 2! 	imes 2! = 4$.Total arrangements $= 4 + 4 = 8$.

The teacher wants to arrange $5$ students on the platform such that the boy $B_1$ occupies the second position and the girls $G_1$ and $G_2$ are always adjacent to each other. Then,the number of such arrangements is

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