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A shelf contains 20 books of which 4 are...

A shelf contains 20 books of which 4 are single volume and the other form sets of 8, 5, and 3 volumes. Find the number of ways in which the books may be arranged on the shelf so that volumes of each set will not be separated. volumes of each set remain in their due order.

Text Solution

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(i) Considering each set as single unit, permutations of 7 units is 7!.
Permutations of books of the set of 8 volumes among themselves is 8!.
Respective permutations of books of the set of 5 volumes is 5! And that of books of 3 volumes is 3!.
By the product rule, total number of permutations is 7! 8! 5! 3!.
(ii) Since the books in a set of books containing any number of volumes can be arranged in due order in 2 ways, the total number of permutations is `7!xx2xx2xx2=8xx7!=8`.
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