Question

There are 3 copies of each of 4 different books.The number of ways that they can be arranged in a shelf is:

• A. $\frac{12!}{(4!{)}^4}$
• B. $\frac{12!}{(4!{)}^3}$
• C. $\frac{12!}{(3!{)}^3}$
• D. $\frac{12!}{(3!{)}^4}$

Answer 1

Answer: (D)

$\frac{12!}{(3!{)}^4}$

No. of ways of arranging n objects, as here a are of one kind, b are of other, c other and so on.............
= $\frac{n!}{a!b!c!...........}$
Total no. $=3+3+3+3$
$=12.$
Ans $=$ $\frac{12!}{3!3!3!3!}$