Applications With Probability: Learn It 3

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]
Jayden has nine paintings and only has room on their wall for four paintings. How many different ways could they select paintings for their wall?