# There are two works each of 3 volumes and two works each of 2 volumes;

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?

Solution:

There are 4 different types of works.

∴ Number of arrangements of these 4 works, taken 4 at a time = 4!

Of these 4 works, two of the works with 3 volumes each can be arranged in 3! ways each and two of the works with 2 volumes each can be arranged in 2! ways.

Total number of arrangements $=4 ! \times(3 ! \times 3 !) \times(2 ! \times 2 !)=3456$