Question

Five different books $(A,B,C,D,E)$ are to be arranged on a shelf. Books $C$ and $D$ are to be arranged first and second starting from the right of the shelf. The number of different orders in which books $A,B$ and $E$ may be arranged is:

• A. $5!$
• B. $3!$
• C. $2!$
• D. $3!\times 2!$

Answer 1

The correct option is B $3!$

Since books $C$ and $D$ are arranged first and second starting from the right of the shelf, therefore, only books $A$, $B$ and $E$ will change order.

Thus, an arrangement problem involves $3$ items and the number of different order is given by $3!$.

Hence, the number of different orders in which books $A$, $B$ and $E$ may be arranged is $3!$.