# A.3 Factorials

A.3 FactorialsFactorials are symbolized by exclamation points (!).

A factorial is a mathematical operation in which you multiple the given number by all of the positive whole numbers less than it. In other words \(n!=n \times (n-1) \times … \times 2 \times 1\).

For example,

“Four factorial” = \(4!=4\times3\times2\times1=24\)

“Six factorial” = \(6!=6\times5\times4\times3\times2\times1)=720\)

When we discuss probability distributions in STAT 200 we will see a formula that involves dividing factorials. For example,

\[\frac{3!}{2!}=\frac{3\times2\times1}{2\times1}=3\]

Here is another example,

\[\frac{6!}{2!(6-2)!}=\frac{6\times5\times4\times3\times2\times1}{(2\times1)(4\times3\times2\times1)}=\frac{6\times5}{2}=\frac{30}{2}=15\]

Also note that 0! = 1

#### Factorials

Here is a brief review of factorials as they will be applied in STAT 200: