Permutations
Before we dive into permutations, it is important to understand how to take a factorial.
factorial
Calculating the factorial is a way to calculate the product of all positive whole numbers up to a given number.
Notation: A factorial is represented by an exclamation mark [latex](!)[/latex] following a number.
[latex]n! = n \cdot (n-1)\cdot (n-2)...1[/latex]
Now that we understand how to take a factorial, lets see how it applies to permutations.
permutation
A permutation is an arrangement of a set of objects in a particular order. In permutations, the order in which the objects are arranged is important.
Notation: The number of permutations of [latex]n[/latex] objects taken [latex]r[/latex] at a time is denoted by [latex]P(n, r)[/latex] and is given by:
[latex]P(n, r) = \frac{n!}{(n-r)!}[/latex]