Factorials

The factorial of a number is the product of all the whole numbers, except zero, that are less than or equal to that number. For example, to find the factorial of 7 you would multiply together all the whole numbers, except zero, that are less than or equal to 7. Like this:
7 x 6 x 5 x 4 x 3 x 2 x 1 = 5,040

The factorial of a number is shown by putting an exclamation point after that number. So, 7! is a way of writing “the factorial of 7” (or “7 factorial”).
Here are some factorials:
1! = 1 = 1
2! = 2 x 1 = 2
3! = 3 x 2 x 1 = 6
4! = 4 x 3 x 2 x 1 = 24
5! = 5 x 4 x 3 x 2 x 1 = 120
6! = 6 x 5 x 4 x 3 x 2 x 1 = 720
7! = 7 x 6 x 5 x 4 x 3 x 2 x 1 = 5,040
8! = 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 40,320
9! = 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 362,880
10! = 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 3,628,800
11! = 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 39,916,800
12! = 12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 479,001,600
Factorials are useful. They can show how many different ways there are to order or arrange a set of things. For example, if you have 5 books on a shelf, and want to know how many different ways there are to order or arrange them, simply find the factorial of 5:
5! = 5 x 4 x 3 x 2 x 1 = 120
This shows that you can arrange 5 books 120 different ways.
Here's a bit of trivia: mathematicians have decided that the factorial of zero, or 0!, is 1. Why? Because you can arrange a set of nothing, an empty set, in just one way—as nothing, an empty set.