How many ways can 6 runners be lined up in a row

Step by step

The question

Question: How many ways can 6 runners be put in a row?

1 Fill the places

2 Write it as a factorial

So the number of ways is 6 × 5 × 4 × 3 × 2 × 1.

6 times 5 times 4 times 3 times 2 times 1 has a short name: 6 factorial.

We write it 6!

Careful!

A runner in one place cannot go in another.

So each place has one fewer.

3 Multiply

6 times 5 is 30.

30 times 4 is 120.

120 times 3 is 360.

360 times 2 is 720.

Times 1 changes nothing.

So there are 720 ways.

4 Check

Let's check the other way round: 1 times 2 is 2, then 6, then 24, then 120, then 720.

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.