A self contains 20 books, of which of 4 are single volumes and the others are books of 8,5and 3 volumes respectively. In how many ways can the books be arranged on the shelf so that volumes of the same workare not separated?

Asked by ashwinikumar59 | 6th Sep, 2010, 05:28: PM

Expert Answer:

Total number of books = 20
Form groups of volumes of same work.
Therefore we have: 4single volumes +Group A(8volumes) +group B(5volumes)+groupC (3volumes)= 4+3= 7 groups.
These 7 groups can be arranged in 7! ways.
 
 
But group A has 8 volumes, so within this group we can arrange in 8! ways. group A has 5 volumes, so within this group we can arrange in 5! ways.
 group A has 3 volumes, so within this group we can arrange in 3! ways.
 
By fundamental theorem, total number of ways = 7!.8!.5!.3!

Answered by  | 7th Sep, 2010, 06:55: AM

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