## How to Use the Factorial Notation

We have had several discussions about the factorial notation, so I think this introduction is a bit late. However, it is important that you know these basic facts in order to perform calculations and understand better in later discussions.

The factorial of a non-negative integer $n$ is the product of all the positive numbers less than $n$. For example, the

$4! = 4 \times 3 \times 2 \times 1 = 24$.

and

$5! = 5 \times 4 \times 3 \times 2 \times 1 = 120$.

In Introduction to Permutations, we have discussed that there are $n!$ ways to arrange $n$ distinct objects into a sequence. For instance, if we have 3 objects namely A, B, and C, then they can be arranged in $3! = 3 \times 2 \times 1 = 6$ ways. The arrangement are as follows:

$ABC, ACB, BAC, BCA, CAB, CBA$.

We have also learned some reasons why mathematicians chose the definition $0! = 1$. » Read more