# Permutation vs. Combination

Main DifferencePermutation and Combination are Mathematical terms. Permutation is the arrangement of objects in which order is priority. Combination is the arrangement of objects in which order is irrelevant. Both are related to each other by formula

P(n,r)=r!⋅C(n,r).

## Difference Between Permutation and Combination

#### Permutation vs. Combination

Permutation is the arrangement of objects in which order is priority or important while Combination is the arrangement of objects in which order is irrelevant.

#### Permutation vs. Combination

Formulae for Permutation is *P*(*n*,*r*)=*n*!**/**(*n*−*r*)! while formula for combination is *C*(*n*,*r*)=*n*! **/** (*n*−*r*)!*r*!

#### Permutation vs. Combination

In permutation order matters while in combination order does not matter.

#### Permutation vs. Combination

To pick up 3 people from a group of 10 then the combination will be 120. For picking a President, VP and a helper from a group of ten people then permutation is 720.

#### Permutation vs. Combination

Picking the two favorite colors from color brochure is permutation while picking any two colors from a color brochure is combination.

#### Permutation vs. Combination

If you pick 1st, 2nd and 3rd place winners, it is permutation and picking the three winners is combination.

#### Permutation vs. Combination

For arranging three objects "ABC", the permutation will give its 6 arrangements while combination is only 1 arrangements.

#### Permutation vs. Combination

For picking two red candies from a box is permutation while picking any two candies from a box is combination.

#### Permutationnoun

One of the ways something exists, or the ways a set of objects can be ordered.

*Which permutation for completing our agenda items makes the most sense?*

#### Combinationnoun

The act of combining, the state of being combined or the result of combining.

#### Permutationnoun

(mathematics) A one-to-one mapping from a finite set to itself.

*This permutation takes each element to the one following it, with the last mapped back to the first.*

#### Combinationnoun

An object formed by combining.

#### Permutationnoun

An ordering of a finite set of distinct elements.

*There are six permutations of three elements, e.g. {abc, acb, bac, bca, cab, cba}.*

#### Combinationnoun

A sequence of numbers or letters used to open a combination lock.

#### Permutationnoun

(music) A transformation of a set's prime form, by applying one or more of certain operations, specifically, transposition, inversion, and retrograde.

#### Combinationnoun

(mathematics) One or more elements selected from a set without regard to the order of selection.

#### Permutationnoun

an event in which one thing is substituted for another;

*the replacement of lost blood by a transfusion of donor blood*

#### Combinationnoun

An association or alliance of people for some common purpose.

#### Permutationnoun

the act of changing the arrangement of a given number of elements

#### Combinationnoun

(billiards) A combination shot; a billiard; a shot where the cue ball hits a ball that strikes another ball on the table.

#### Permutationnoun

complete change in character or condition;

*the permutations...taking place in the physical world*

#### Combinationnoun

A motorcycle and sidecar.

#### Permutationnoun

act of changing the lineal order of objects in a group

#### Combinationnoun

A rapid sequence of punches or strikes in boxing or other combat sports.

#### Combinationnoun

a collection of things that have been combined; an assemblage of separate parts or qualities

#### Combinationnoun

a coordinated sequence of chess moves

#### Combinationnoun

a sequence of numbers or letters that opens a combination lock;

*he forgot the combination to the safe*

#### Combinationnoun

a group of people (often temporary) having a common purpose;

*they were a winning combination*

#### Combinationnoun

an alliance of people or corporations or countries for a special purpose (formerly to achieve some antisocial end but now for general political or economic purposes)

#### Combinationnoun

the act of arranging elements into specified groups without regard to order

#### Combinationnoun

the act of combining things to form a new whole

### What is Permutation?

Permutation is the arrangement of objects in which order is priority or important. It refers to an arrangement of a subset of a given size in combinations. It is the choice of r objects from a set of n objects without replacement and order of objects matters. Its formula is *P*(*n*,*r*)=*n*!**/**(*n*−*r*)!. If you pick 1st, 2nd and 3rd place winners, it is permutation.

### What is Combination?

Combination is the arrangement of objects in which order is irrelevant. It refers to number of subsets of a set of objects. It is the choice of r objects from a set of n objects without replacement and order of objects does not matter. Its formula is *C*(*n*,*r*)=*n*! **/** (*n*−*r*)!*r*!. Picking the three winners is combination.