• 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:

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