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A shelf contains 20 books,of which of 4 are single volumes and the others are books of 8,5,3 volumes respectively,in how many ways can the books be arranged on the shelf so that volumes of the same work are not seperated..
answer=4!
String the volumed books.
Now you have 4(single volume)+3(stringed volumes) = 7 units.
The can permutate in 7! ways.
The volumes themselves in each set(stringed) can permutate in 8!,5! and 3! ways respectively.
Required Number of permutations = 7!*(8!*5!*3!)
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