# Permutation vs. Combination: What's the Difference?

Edited by Huma Saeed || By Sumera Saeed || Updated on October 15, 2023
Permutation is the arrangement of items in a specific order, while combination is the selection of items without considering order.

## Key Differences

Permutation refers to the arrangement of items in a specific sequence or order. This means the order in which the items are arranged is important. For example, the permutations of the letters A, B, and C are ABC, ACB, BAC, BCA, CAB, and CBA. Each arrangement is considered unique in permutation.
Sumera Saeed
Oct 15, 2023
Combination, on the other hand, deals with the selection of items without considering their order. Here, it's the group of items that matters, not the sequence in which they appear. For the same set of letters, A, B, and C, the combinations are ABC, AB, AC, and BC. Note that AC and CA are the same combination because order does not matter.
Sumera Saeed
Oct 15, 2023
It's easier to think of permutation as a specific sequence. For example, consider a race. The order in which the participants finish (first, second, third, etc.) is a permutation. In contrast, combination could be likened to a team selection, where the members of the team are important, but their sequence is not.
Sumera Saeed
Oct 15, 2023
Both permutation and combination are foundational concepts in the field of combinatorics, a branch of mathematics that deals with counting and arrangements. While permutations focus on sequences and order, combinations are all about groups and selection.
Sumera Saeed
Oct 15, 2023

## Comparison Chart

### Basic Definition

Order matters.
Order doesn't matter.
Sumera Saeed
Oct 15, 2023

### Example (ABC)

ABC, ACB, BAC, BCA, CAB, CBA.
ABC, AB, AC, BC.
Sumera Saeed
Oct 15, 2023

### Grammar Usage

"The permutation of words in the sentence changes its meaning."
"The combination of colors in the painting is stunning."
Sumera Saeed
Oct 15, 2023

### In Mathematics

NPr = n! / (n-r)!
NCr = n! / (r! * (n-r)!)
Sumera Saeed
Oct 15, 2023

### Real-Life Scenario

Arranging books on a shelf.
Selecting books to read from a shelf.
Harlon Moss
Oct 15, 2023

## Permutation and Combination Definitions

#### Permutation

Permutation is the act of altering the order of a set.
The music playlist has several permutations, depending on the mood.
Sara Rehman
Oct 15, 2023

#### Combination

Combination represents the total ways items can be grouped together.
There are 3 combinations for the colors red, blue, and green taken two at a time.
Sara Rehman
Oct 15, 2023

#### Permutation

Permutation signifies a distinct and unique arrangement within a set.
Each permutation of the puzzle pieces results in a different picture.
Janet White
Oct 15, 2023

#### Combination

Combination deals with selection without focusing on sequencing.
The combination of notes creates a beautiful chord in music.
Harlon Moss
Oct 15, 2023

#### Permutation

Permutation denotes the total number of ways items can be sequenced.
There are 6 permutations for the three colors red, blue, and green.
Harlon Moss
Oct 15, 2023

#### Combination

Combination is the act of choosing elements from a larger set.
The combination of ingredients makes the dish unique.
Aimie Carlson
Oct 15, 2023

#### Permutation

Permutation is the arrangement of objects in a specific order.
The permutation of the numbers 1, 2, and 3 are 123, 132, 213, 231, 312, and 321.
Huma Saeed
Oct 15, 2023

#### Combination

Combination is the selection of items without regard for order.
The combination of fruits for the salad includes apples, bananas, and oranges.
Huma Saeed
Oct 15, 2023

#### Permutation

Permutation involves both selection and arrangement of items.
The permutation of letters in a word game can lead to various outputs.
Janet White
Oct 15, 2023

#### Combination

Combination signifies a collection or assortment of items.
Each combination of team members brings different strengths.
Sumera Saeed
Oct 15, 2023

#### Permutation

The process of altering the order of a given set of objects in a group.
Sumera Saeed
Aug 27, 2015

#### Combination

The act of combining or the state of being combined.
Sumera Saeed
Aug 27, 2015

#### Permutation

The result of such a process; a rearrangement or recombination of elements
Permutations of gene order.
Sumera Saeed
Aug 27, 2015

#### Combination

The result of combining.
Sumera Saeed
Aug 27, 2015

## FAQs

#### How is combination different from permutation?

In combination, order doesn't matter, while in permutation, order is important.
Huma Saeed
Oct 15, 2023

#### Can the terms permutation and combination be used interchangeably?

No, because they refer to different mathematical concepts.
Sumera Saeed
Oct 15, 2023

#### How many permutations are there for a set of n items taken r at a time?

There are nPr = n! / (n-r)! permutations.
Aimie Carlson
Oct 15, 2023

#### How many combinations are there for a set of n items taken r at a time?

There are nCr = n! / (r! * (n-r)!) combinations.
Harlon Moss
Oct 15, 2023

#### Why is the order important in permutation?

Because permutation considers each unique arrangement as distinct.
Aimie Carlson
Oct 15, 2023

#### Can a set have the same permutation and combination value?

Yes, when the set is taken all at once, its permutation and combination values are both 1.
Janet White
Oct 15, 2023

#### Which is more complex to calculate, permutation or combination?

Permutation is generally more complex due to the importance of order.
Harlon Moss
Oct 15, 2023

#### Why is there no consideration of order in combinations?

Because combinations focus on groupings, not sequences.
Harlon Moss
Oct 15, 2023

#### Does changing the order of items affect combination?

No, order doesn't matter in combinations.
Aimie Carlson
Oct 15, 2023

#### What is the significance of permutation in real life?

It can represent scenarios like race outcomes, password arrangements, and more.
Sumera Saeed
Oct 15, 2023

#### Is permutation always greater than combination for the same set?

Yes, because permutation considers different orders, while combination does not.
Aimie Carlson
Oct 15, 2023

#### Can a single item have permutations?

Yes, but there's only one permutation for a single item.
Janet White
Oct 15, 2023

#### How are permutation and combination used in statistics?

They help in calculating probabilities and outcomes in various scenarios.
Aimie Carlson
Oct 15, 2023

#### Are permutation and combination concepts only applicable in mathematics?

No, they are used in various fields like computer science, statistics, and everyday life scenarios.
Aimie Carlson
Oct 15, 2023

#### How is combination used in real-life scenarios?

Combination is used in scenarios like team selections, food recipes, and more.
Aimie Carlson
Oct 15, 2023

#### What does "n!" mean in permutation and combination formulas?

"n!" means n factorial, which is the product of all positive integers up to n.
Janet White
Oct 15, 2023

#### Are there any real-life scenarios where both permutation and combination apply?

Yes, such as selecting and arranging team members for specific positions.
Sara Rehman
Oct 15, 2023

#### What is a permutation?

A permutation is the arrangement of objects in a specific order.
Sumera Saeed
Oct 15, 2023

#### Is every permutation also a combination?

Yes, but not every combination is a permutation.
Aimie Carlson
Oct 15, 2023

#### How does changing the order of items affect permutation?

Changing order creates a new permutation.
Janet White
Oct 15, 2023