GATE ECE 2019 | GA | Question: 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. $120$

Comments

i guess these types of questions are dangerous for overthinkers.

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 $(B).$

Answer 2

Placing 3 objects in 3 available space (since out of 5 last 2 from right are occupied) giving 3! ways to arrange i.e 6 

 

Option B is correct.

Answer 3

You have total of 5 books, out of these 5 books,

1. 2 books are selected as first and second position and
2. The remaining books are 3 i.e., P, Q & T
3. Total no.of orders in which P, Q & T can be arranged is 3! i.e., 6

Answer = B(6)

Answer 4

R and S arranged 1st and 2nd Respectively  from Right Side 

 

 ------     --------    --------       S      R     For P,Q,T we have 3*2 *1 =6 ways