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?

Explanation

Let us consider the four works as four groups.
Group I and II have `3` works each and groups III and IV
have `2` volumes each.
Number of ways of arranging `4` groups in a shelf is `4_(P_4)`​=4!=24 ways.

Volumes in each groups can themselves be arranged.

Group I and II can be arranged each in `3_(P_3​)`=3!=6 ways.
Group III and IV can be arranged each in ` 2_(P_2)​`=2!=2 ways.

Hence, total number of arrangements =`24xx6xx6xx2xx2=3456` ways.