Question

There are $3$ copies each of $4$ different books. The number of ways they can be arranged on a shelf is?

• A. $369600$
• B. $400400$
• C. $420600$
• D. $440720$

Answer 1

The correct option is A

$369600$

Find the number of arrangements based on given information

Given: $3$ copies each of $4$ different books.

Total number of books $=3\times 4=12$

Required number of arrangements

$$\begin{gathered} =\frac{12!}{3!\times 3!\times 3!\times 3!} \\ =\frac{12!}{{\left(3!\right)}^4} \\ =369600 \end{gathered}$$

Hence, option A is correct .