Question

Five books need to be placed on a shelf.

You randomly arrange the books on the
shelf from left to right.

Answer 1

There are 120 different ways to arrange 5 books on a shelf.

In how many different ways can these books be arranged on the shelf?

When you arrange 5 books on a shelf

• You have 5 choices for the first book.
• For the second book, you only have 4 books left, so there are only 4 choices for the second book.

So far, you have 5 x 4 = 20 choices.

• For the third book, you only have 3 books left, so there are only 3 choices.

So far, you have 5 x 4 x 3 = 60 choices.

You can continue doing this for the fourth and fifth books.

The total number of choices is 5 x 4 x 3 x 2 x 1 = 120.

Hence, there are 120 different ways to arrange 5 books on a shelf.

Question

Five books need to be placed on a shelf. You randomly arrange the books on the shelf from left to right.

In how many different ways can these books be arranged on the shelf?