# Difference Between Permutation and Combination

## Core difference

Permutation and combination are mathematical terms. Permutation is the arrangement of objects in which the order is the priority. Combination is the arrangement of objects in which the order is irrelevant. Both are related to each other by the formula *P* ( *n* , *r* ) = *r* ! ⋅ *C* ( *n* , *r* ).

## What is permutation?

Permutation is the arrangement of objects in which the order is a 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 the order of the important objects. Its formula is *P* ( *n* , *r* ) = *n* ! **/** ( *n* – *r* )!. If you pick the 1st, 2nd, and 3rd place winners, it’s a permutation.

## What is the combination?

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

## Key differences

- Permutation is the arrangement of objects in which the order is paramount or important, while combination is the arrangement of objects in which the order is irrelevant.
- The formulas for the permutation are
*P*(*n*,*r*) =*n*!**/**(*n*–*r*)! while the formula for the combination is*C*(*n*,*r*) =*n*!**/**(*n*–*r*)!*r*! - In the permutation order it matters, while in the combination order it doesn’t matter.
- To elect 3 people out of a group of 10, the combination will be 120. To elect a president, vice president, and assistant out of a group of ten people, the permutation is 720.
- Choosing your two favorite colors from a color brochure is a permutation, while choosing any two colors from a color brochure is a combination.
- If you pick the 1st, 2nd, and 3rd place winners, it’s permutation, and picking all three winners is combination.
- To order three “ABC” objects, the permutation will give their 6 arrangements while the combination is only 1 arrangement.
- To pick any two red candies from a box is permutation, while picking any two candies from a box is combination.