Question

There are two works each of 3 volumes and two works each of 2 volumes ; In how many ways can the 10 books be placed on a shelf so that the volumes of the same work are not separated?

Answer 1

Let, $w_1,w_2,w_3,and{w}_4$ be 4 words, where $w_1,w_2$ have 3 volumes each and $w_3,w_4$, have 2 volume each.
These 4 works can be arranged in 4! ways.
Now,
volumes of $w_1$ can be arranged in 3! ways.
volumes of $w_2$ can be arranged in 3! ways.
volumes of $w_3$ can be arranged in 2! ways.
And volumes of $w_4$ can be arranged in 2! ways
$\therefore$ Total number of ways to arrange all books = 4! $(3!\times 3!\times 2!\times 2!)$
= $24\times 6\times 6\times 2\times 2$ = 3456.