The Permutation Formula: Understanding Your Options

Permutations are an important part of statistics and probability. It allows us to come up with exact numbers for large groups of people. In many ways permutations are very similar to combinations, and outside of mathematics the two are often used interchangeably, but when it comes to mathematics the two are very different, and you have to understand them both to get a strong grasp on things, such as financial analysis.

When studying statistics and probability, the permutation formula is one of the first concepts you will learn. Permutations help you arrange and come up with all possible orders you can do something with the qualification of the order mattering, which is what makes it different from combinations. You can study combinations and permutations by checking out the Udemy course Workshop in Probability and Statistics.

What Are Permutations?  

Simply put, permutations – as mentioned before – are all the possible ways you can do something; unlike a combination though the order of each item always matters.

For example, say we wanted to order 3 people out of 8, but the order of the people mattered. We would first look at all the options or in this instance 8 people and then take one at a time until we reached our goal of three.

This is called a factorial, and it is used for situations like this. The equation of this particular instance or factorial is represented like so n! or 8!. When doing a factorial, finding the result is easy, you just do n * n – 1 * n – 2 * n – 3, and so on. So in the case of 8 factorial we will get 8 * 7 * 6 * 5 * 4…etc.

This is not the proper solution to the problem though, because 8 factorial does not provide us with all the permutations of 3 people in the set, but all the permutations in the set in general.

In order to get this value we have to “stop” the factorial at 5 or after the first three numbers.

The way we do this is by dividing the term by 5 factorial, and we then get the following equation.

8!/5!. This equation equals out to be 8 * 7 * 6 * 5!/5!. Since the two 5 factorials factor out into one you are left with 8 * 7 * 6, and when you multiply those terms together you have your answer.

The Permutation Formula

The example presented before provided us with information on how to work the permutation formula, but not exactly what it is. The permutation formula for the example above would be 8!/(8 – 3)!

This is just for that one equation though, the true formula for all permutation formulas is below.

Explaining the formula is simple, especially now that you know how it all works. For example, n represents all of the numbers in the set. In case of the example n was the number 8. On the other hand k represents all of the numbers we want to get for each group of people within the set. In the example above we wanted 3 people from the group of 8, which means that k represented 3.

Imagine a scenario where there were 11 campers and you wanted to find all the possible groups of 5 campers to go out and find firewood. You would do the same as we did in the first example above. You would set n as 11 to represent all of the campers, and you would set k as the number of campers you want for each group.

The problem would end up looking like 11!/(11-5)! Or 11!/6!.

Statistics and probability are an important part of mathematics; you will even see it on tests like your SATs. If you want to be prepared, check out the SAT Math course offered by Udemy.

Why Would You Use Permutations

Permutations are introduced to you early in Statistics & Probability courses and they can be used for a large part of your life, especially if you’re working in a career that has a lot of emphasis on ordered sets and analysis. The Udemy course Introductory Statistics, Part 1: Descriptive Statistics is a great way to get you started. Once you get the hang of it, you will be able to do more complex forms of statistical analysis, which includes Inferential Statistics that Udemy has a great course on if you want to increase your statistical analysis skills.