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 $=4 ! \times(3 ! \times 3 !) \times(2 ! \times 2 !)=3456$
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