Question

A shelf contains $20$ different books of which $4$ are in single volume and the others form sets of $8$, $5$ and $3$ volumes respectively. Number of ways in which the books may be arranged on the shelf, if the volumes of each set are together and in their due order is?

• A. $20!$
• B. $7!$
• C. $8!$
• D. $8\times 7!$

Answer 1

The correct option is D $8\times 7!$

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$=2\times 2\times 2$

Number of ways in which the books may be arranged on the shelf, if the volumes of each set are together and in their due order $=7!\times 2\times 2\times 2=8\times 7!$