How many ways can 7 photos be arranged in a row

Step by step

The question

Question: How many ways can 7 photos be put in a row?

1 Fill the places

2 Write it as a factorial

So the number of ways is 7 × 6 × 5 × 4 × 3 × 2 × 1.

7 times 6 times 5 times 4 times 3 times 2 times 1 has a short name: 7 factorial.

We write it 7!

Careful!

A photo in one place cannot go in another.

So each place has one fewer.

3 Multiply

7 times 6 is 42.

42 times 5 is 210.

210 times 4 is 840.

840 times 3 is 2520.

2520 times 2 is 5040.

Times 1 changes nothing.

So there are 5040 ways.

4 Check

Let's check the other way round: 1 times 2 is 2, then 6, then 24, then 120, then 720, then 5040.

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.