Chapter 9.1, Problem 3E

Solution

To state: The numbers of ways in which five books can be arranged from left to right on a bookshelf.

The resultant answer is 120 ways.

Given information:

Five books have to be arranged from left to right on a bookshelf.

Explanation:

Number of books is: 5

Any of the 5 books can be placed to the left side. Thus there are 5 ways in which a book can be placed to the left.

Now 4 books are remaining, the second book can be placed to the right of the first book in 4 ways.

Now 3 books are remaining, the third book can be placed to the right of the second book in 3 ways.

Now 2 books are remaining, the fourth book can be placed to the right of the third book in 2 ways.

At last there is 1 book left it can be placed to the right of the fourth book in 1 way.

The number of ways is:

  $5\cdot 4\cdot 3\cdot 2\cdot 1=120$

Therefore, there are 120 ways in which five books can be arranged from left to right on a bookshelf.