The difference between permutation and combination is that, for permutations, the order of the elements is taken into consideration and for combinations, the order of the elements does not matter. For example, organizing objects is an example of permutations, but selecting a group of objects is an example of combinations.

##### ALGEBRA

**Relevant for**…

Learning the difference between permutations and combinations.

##### ALGEBRA

**Relevant for**…

Learning the difference between permutations and combinations.

## Definitions of permutations and combinations

### Permutations

A permutation can be defined as the action of organizing a few or all the elements of a set in a specific order. The process of ordering out-of-order items is called a permutation.

### Combinations

A combination is a process of selecting the elements or objects of a set in a way that, unlike permutations, the order does not matter. This refers to the combination of elements taken from a set without any repetition.

## What are the differences between permutations and combinations?

In the following table, we can compare the characteristics of permutations and combinations and we can observe their differences:

Permutations | Combinations |

Permutations are the different ways to organize a set of objects in sequential order. | Combinations are various ways of choosing elements from a larger set of objects without considering the order. |

The order is important. | The order is not important. |

It refers to the organization of objects. | It does not denote the organization of objects. |

Multiple permutations can be derived from a single combination. | From one permutation, only one combination can be derived. |

They can be defined as ordered elements. | They can be defined as sets without order. |

## Examples of permutations and combinations

### EXAMPLES

Suppose we have to find the total number of probable samples of two objects from a set of three objects A, B, C. First of all, we have to determine whether this is a permutations problem or a combinations problem. For this, all we have to do is find out if the order is relevant or not.

If the order is important, then we have a permutations problem. In this case, the possible number of samples will be AB, BA, BC, CB, AC, CA. When we have permutations, we consider AB and BA as different. Similarly, BC and CB, AC and CA are different.

If the order is not important, then we have a problem with combinations. In this case, the possible samples are AB, BC, and AC.

## Frequently asked questions

### What are permutations and combinations?

A permutation is considered a method to organize a set of elements in order. A combination is considered as the selection of a set of elements, where the order is not important.

### What are the formulas for combinations and permutations?

The permutations formula is $latex _{n}{{P}_{r}}=\frac{{n!}}{{({n-r})!}}$.

The combinations fomrula is $latex _{n}{{C}_{r}}=\frac{{n!}}{{( {n-r})!r!}}$.

### What is an example of permutations?

The organization of numbers, letters, or other objects are examples of permutations.

### What is an example of combinations?

Selecting objects from a list, selecting people from a group are examples of combinations.

## See also

Interested in learning more about algebraic expressions, permutations, and combinations? Take a look at these pages:

### Learn mathematics with our additional resources in different topics

**LEARN MORE**