# A.3 Factorials

A.3 Factorials

Factorials 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:

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