# Factorials

When mathematicians write 5! the exclamation mark does not express surprise or excitement. It is just a convenient
way of writing 'factorial 5'. This means the number you get by multiplying together
–

1 × 2 × 3 × 4 × 5

– which comes to 120.

Factorials of other numbers are calculated in the same way. Factorial 10 or 10! is –

1 × 2 × 3 × 4 × 5 × 6 × 7 × 8 × 9 × 10

– which comes to quite a large number, 3,628,800.

Factorials are useful in working out the number of different ways you can arrange things. Factorial *n*
is the number of ways *n* things can be arranged in a line. So if you had
five garden gnomes in your front garden, they could be lined up in 5! or 120
different ways.

In the same way, eleven in a football team can stand in a row in 11! ways and a deck of 52 playing cards can be ordered in 52! different ways which is a huge number with 68 digits.

Here are the first ten
factorials –

1! = 1

2! = 2

3! = 6

4! = 24

5! = 120

6! = 720

7! = 5,040

8! = 40,320

9! = 362,880

10! = 3,628,800

Based on the book *Numbers: Facts, Figures & Fiction*.