# Factorials

 From: E Crane Date: 17 Feb 1999 Subject: What does "!" mean? Dear Maths Help, I hope you do not mind me troubling you with a question. I am seventy-nine years old, and try to keep my mind active by doing mathematics problems and "surfing" the internet. My question is: what does the exclamation mark mean when it is written after a number? I came across it in the answer section to a book of mathematical puzzles.

### Maths Help suggests:

The exclamation mark symbol is pronounced "factorial" when used in mathematics. It is shorthand for what you get when you multiply the given number (which must be a positive whole number) by all the smaller whole numbers down to 1.
For example:

So you can see that factorials get quite big very quickly.

Two "special cases" are:

Factorials have several applications. The most common one is:
 N different items can be placed in a row in N! different ways
For example, three different colour balls can be placed in a row in 3! = 6 different ways, as shown below: