# Permutation and Combination Calculator

Created by Wei Bin Loo
Reviewed by Julia Żuławińska
Last updated: Jun 05, 2023

Table of contents:

With this permutation and combination calculator, we aim to help you to calculate the permutations and combinations of the given number of objects. This calculator will help you know what the possible permutations and combinations are.

We have written this article to help you understand the difference between permutations and combinations and their respective definitions. We will also demonstrate some calculation examples to help you understand the permutation and combination formulas. Moreover, our calculator also displays the possible permutations and combinations to help you understand the concept easier.

## What are permutations and combinations?

Given the sample size, permutation is the number of ways that a certain number of objects can be arranged in a sequential order. On the other hand, a combination is defined as the number of ways that a certain number of items can be grouped together, given the sample size.

Both of these metrics are useful in calculating probabilities. Have you ever wondered what your chances of winning a lottery are? In order to win a lottery, you need to have the correct numbers in the right sequence. Hence, to answer this question, you will need to understand permutation. A similar concept can also be applied to combinations.

## How to calculate permutations and combinations? The formula for combinations and permutations

To understand the calculation for permutations and combinations, let's look at some examples below.

For permutation, let's assume the following:

• Calculation: Permutation
• The total number of objects, n: 6
• Sample size, r: 3

You can calculate the number of possible permutations in three steps:

1. Determine the total number of objects

This is the total number of objects that you possess. In this example, n is 6.

1. Determine the sample size

This is the size of the permutations that you wish to compute. The r in this example is 3.

1. Calculate the number of possible permutations

This can be calculated using the permutation formula:

nPr = n! / (n-r)!

The number of possible permutations, nPr, is 6! / (6 - 3)! = 120.

For combination, let's assume the following:

• Calculation: Combination
• The total number of objects, n: 7
• Sample size, r: 4

You can calculate the number of possible permutations in three steps:

1. Determine the total number of objects

The definition of the total number of objects is the same as the one in permutation. In this example, n is 7.

1. Determine the sample size

Similarly, this is the size of the combinations that you wish to compute. The r in this example is 4.

1. Calculate the number of possible combinations

This can be calculated using the combination formula:

nCr = n! / (r!(n-r)!)

The number of possible combinations, nCr, is 7! / 4! * (7 - 4)! = 35.

If the permutations and combinations formula still seems confusing, don't worry; just use our calculator for the calculations. We will even show you the permutation and combinations examples.

## What is the difference between permutation and combination?

Now that we understand the definitions of permutations and combinations, let's discuss what the difference between permutations and combination is.

There are two main differences between combinations and permutations:

• As permutation calculates the number of possible ways to arrange a certain number of items, different sequences with the same items are considered different. For example, ABC and BCA are two different permutations. Whereas for combination, they are considered the same.

• Permutation and combination are meant to solve different probability problems. While permutation deals with sequential problems like the lottery, combinations are mostly used to solve problems that ignore sequence.

To understand more about this topic, I strongly recommend you to check out our other calculators on this topic:

## FAQ

### What is a combination?

A combination is defined as the number of ways that it is possible to group n objects in r size. The order of the items in the group does not matter.

### What is a permutation?

A permutation is defined as the number of possible ways that in arranging n object in r size. The order of the items in the group matters.

### How to calculate a combination?

You can calculate a combination in three steps:

1. Determine the total number of objects, n
2. Determine the sample size, r
3. Apply the combination formula: nCr = n! / (r!(n-r)!)

### How to calculate a permutation?

You can calculate a permutation in three steps:

1. Determine the total number of objects, n
2. Determine the sample size, r
3. Apply the combination formula: nPr = n! / (n-r)!

### Can combination and permutation be negative?

No, combination and permutation cannot be negative. Even with one sample, the combination and permutation should be at least 1.

Wei Bin Loo
Set of objects
Total number of objects n
Sample size r
Number of selections
Permutations
Combinations
Permutation / Combination generator
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Permutations
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