GATE2019 EC: GA-4

Question

Five different books $(P, Q, R, S, T)$ are to be arranged on a shelf. The books $R$ and $S$ are to be arranged first and second, respectively from the right side of the shelf. The number of different orders in which $P, Q$ and $T$ may be arranged is ______.

• A. $2$
• B. $6$
• C. $12$
• D. $120$

Answer 1

$$\underbrace{\underline{}\;\underline{}\;\underline{}}_{3!\text{ ways}}\;\boxed{\underline{S}\;\underline{R}}$$
As positions of $R$ and $S$ are fixed at first and second from right, so $ P, Q,$ and $T$ can be arranged in three possible places.
Hence, the total possible arrangements $={3!}=6$
Correct option is $(B).$