Question

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

• A. $40320$
• B. $40300$
• C. $40220$
• D. $40200$

Answer 1

Answer: (A)

$40320$

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.$=2\times 2\times 2$

so total $=7!\times 2\times 2\times 2$

$=40320$ ways