Have you ever wondered what the difference is between permutations and combinations?
Jenn, Founder Calcworkshop®, 15+ Years Experience (Licensed & Certified Teacher)
A permutation is an arrangement of items in a particular order. In other words, Placement or Position matter.
For example, imagine you are trying to arrange pictures on a wall. This means that the arrangement of the pictures is dependent on order: 1st, 2nd, 3rd, etc.
A combination is an arrangement of items without regard to order. In other words, you Couldn’t Care Less about the order you’re just interested in counting groups.
So to review…when the order doesn’t matter, we use Combinations and when the order does matter it is a Permutation, as Math is Fun nicely summarizes.
Differences between Permutations and Combinations
Both permutations and combinations are grounded in the fundamental counting principal which proves that multiplication is a great way to quickly count the number of ways a certain thing can happen.
Furthermore, both combinations and permutations will utilize factorials. A factorial is the multiplication of a series of descending natural numbers and helps us in creating the formulas for how to calculate permutations and combinations.
Together we will learn the notation used for permutations and combinations and how to apply these formulas for when repetition is and isn’t allowed.
What this means, is that sometimes we are allowed to repeat numbers or items, and other times we must reduce the number of available choices each time. This happens when you are playing card games, arranging letters in a word where you can only use each letter once, or when you are trying to select positions.
Formulas for Finding Permutations and Combinations
We will also learn how to determine when to use permutations or combinations without repetition based on the given problem, and be able to quickly establish the number of possible outcomes.
Permutations and Combinations – Video
Get access to all the courses and over 450 HD videos with your subscription
Monthly and Yearly Plans Available
Still wondering if CalcWorkshop is right for you?
Take a Tour and find out how a membership can take the struggle out of learning math.