Five students are to be arranged on a platfor | 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 students are $4$ (including $G_1$ and $G_2$).Si

Vedclass · Accepted Answer

$8$

Vedclass · Answer

(C) There are $5$ positions in total. The boy $B_1$ is fixed at the $2^{	ext{nd}}$ position.Remaining students are $4$ (including $G_1$ and $G_2$).Since $G_1$ and $G_2$ must be adjacent,we treat $(G_1, G_2)$ as a single unit.Now we have $3$ units to arrange in the remaining $4$ positions: the unit $(G_1, G_2)$ and the $2$ other students.However,the $2^{	ext{nd}}$ position is already occupied by $B_1$. The available positions are $1^{	ext{st}}, 3^{	ext{rd}}, 4^{	ext{th}}, 5^{	ext{th}}$.If we place the unit $(G_1, G_2)$ in positions $(3, 4)$ or $(4, 5)$,we have $2$ ways to place the unit.Within the unit,$G_1$ and $G_2$ can be arranged in $2! = 2$ ways.The remaining $2$ students can be arranged in the remaining $2$ positions in $2! = 2$ ways.Total arrangements $= 2 	imes 2 	imes 2 = 8$.

Five students are to be arranged on a platform such that the boy $B_1$ occupies the second position and the girl $G_1$ is always adjacent to the girl $G_2$. Then,the number of such possible arrangements is

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