# There are three copies each of 4 different books.

Question:

There are three copies each of 4 different books. In how many ways can they be arranged in a shelf?

Solution:

Total number of books = 12

$\therefore$ Required number of arrangements $=$ Arrangements of 12 things of which each of the 4 different books has three copies $=\frac{12 !}{3 ! 3 ! 3 ! 3 !}=\frac{12 !}{(3 !)^{4}}$