Below is a *combination calculator*, which will calculate the number of combinations, or sets you can choose from a larger whole. Enter the total things in the set **n** and the number you need in your sample **r** and we'll compute the number of combinations.

*If you care about the order of the selection, use the permutation calculator (or change the input in the tool).*

## Combination Calculator

**Table of Contents**show ▼

## What is a Combination?

A *combination* is a unique subset chosen from a larger whole. A combination doesn't care about the order of the elements you choose. That is, if you chose **A and B** from a set of **A, B, and C**, it's the same as picking **B and A**.

## Combinations vs. Permutations

*Combinations* are related to *permutations*. In permutations you do care about the order of a set, however.

As I joked in the permutation calculator, "a combination lock is a lie". If your combo is 4-26-3 you have to enter it in exactly that order to open the lock. They should be called *permutation locks*.

## Formula for Combinations

The formula for the calculating combinations is:

Where:

- n – the size of the set
- r – the size of the subset you are choosing

Compared to the permutation formula, there is an extra term for the factorial of the subset in the denominator.

### Example Combination Calculation

Let's say you have 4 letters: **A, B, C, D**

How many combinations are there when choosing a 2 letter subset?

This is easy to verify. The only possible 2 letter subsets from A, B, C, and D are:

- AB AC AD
- BC BD
- CD

There's no other way to choose combination subsets. For example, DC is the same as CD.

## Using the Combination Calculator

To compute the total number of combination, first enter "n", the total number of things in your set. Next, enter "r" which is how large of a subset you would like to calculate.

After that, leave the "Permutations or Combinations?" pulldown menu on **Combinations**, unless you do care about order.

Hit Calculate and we'll let you know how many combinations are possible.

*Having fun? Visit our other calculators and tools.*