Question

There are two books each of 5 volumes and two books each of two volumes. In how many ways can these books be arranged in a shelf so that the volumes of the same book should remain together

Answer 1

13,82,400  Ways books be arranged in a shelf so that the volumes of the same book should remain together

Step-by-step explanation:

There are two books each of 5 volumes and two books each of two volumes

Total Book = 4

4 books can be arranged in 4!  = 24 Ways

Each book of 5 Volumes can be arranged in 5!  Ways

Each Book of 2 Volumes can be arranged in 2! ways

Total ways = 41 * 5! * 5! * 2! * 2!

= 13,82,400  Ways

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Answer 2

A shelf contains 20 books, of which 4 are single volumes and the others are books of 8, 5 and 3 volumes respectively. The number of ways the books can be arranged on the shelf so that volumes of the same work are not separated is ?

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