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?

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!