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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..

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..

Grade:12

3 Answers

Chetan Mandayam Nayakar
312 Points
11 years ago

answer=4!

Jit Mitra
25 Points
11 years ago

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!)

subiksha
13 Points
4 years ago
we have 4(single volume) + 3(stringed volumes) =7 units  which can be permuted in 7! ways.
 
the books in stringed volume can be arranged in 2 ways(ascending or descending order as order of the books cant be  changed in stringed volume)
therfore we can repeat the same for all the 3 stringed volumes = 2*2*2 = 8.
Therefore no of ways of permuting books = 7! *8  =8!
 ANSWER = 8!

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