# Difference between Permutation and Combination

### Permutation

** The permutation is an action of arranging all or a few members of a set within a linear order**. In other words, it is a selection process in which sequence matters. If a set is already in sequence, then the rearrangement of its elements is called the

*process of permuting.*For instance: the permutations of the numbers in a small set {1, 2, 3} are:

(1,2,3), (1,3,2), (3,1,2), (3,2,1), (2,3,1), (2,1,3)

**Formula:**

Here,

**n=** is the total number of elements in a set.

**r=** the number of selected objects

**!=** factorial

### Combination

** The combination is a way of selecting a given number of elements from a bulk collection without regard of their arrangement**. In other words, in combination, items can be selected in any order.

**Formula:**

Here,

**n=** is the total number of elements in a set.

**r=** the number of selected objects (the order does not matter)

**!=** factorial

**Comparison between permutation and combination **

Basis |
Permutation |
Combination |

Meaning |
A permutation is an action of arranging all or a few members of a set within a linear order. | The combination is a way of selecting a given number of elements from a bulk collection without regard to their arrangement. |

Order |
In permutation, order of the elements is necessary. | In combination, order of the elements is not necessary. |

Formula |
permutation formula is: |
Combination formula is: |

Denotes |
Permutation denotes several ways to arrange things, people, digits, alphabets, colors, etc. | Combination denotes several ways of selecting menu items, food, clothes, subjects, etc. |