Question

A shelf contains 20 books, of which 4 are single volume and the others are 8,5 and 3 volumes respectively. In how many ways can these books be arranged on the shelf so that the order of the volumes of same work is maintained ?​

Answer 1

We know that the same work should not be separated,

so lets consider the 8,5 and 3 volumes as 1 unit each and 4 volumes as 4 units

so,

we have 7 units that means 7! ways to arrange.

Each of these 8,5 and 3 volumes can be arranged either in ascending or descending order.=2×2×2

so total =7!×2×2×2

=40320 ways