How many ways can 5 books be put in a row

Step by step

The question

Question: How many ways can 5 books be put in a row?

1 Fill the places

2 Write it as a factorial

So the number of ways is 5 × 4 × 3 × 2 × 1.

5 times 4 times 3 times 2 times 1 has a short name: 5 factorial.

We write it 5!

Careful!

A book in one place cannot go in another.

So each place has one fewer.

3 Multiply

5 times 4 is 20.

20 times 3 is 60.

60 times 2 is 120.

Times 1 changes nothing.

So there are 120 ways.

4 Check

Let's check the other way round: 1 times 2 is 2, then 6, then 24, then 120.

The same.

So the answer is right!

Let's look back.

First: fill the places.

Then: write it as a factorial.

Then: multiply.

Last: check.