Permutation vs Combination

Last Updated : 8 Jun, 2026

Permutation and Combination are the most fundamental concepts in mathematics related to picking items from a group or set.

  • Permutation is the arrangement of items in which the order of selection matters.
  • Combination is selecting items without considering order.
permutation_combination

The key differences between Permutation and Combination are as follows:

Feature

PermutationCombination

Definition

Arrangement of objects in a specific order.Selection of objects without regard to order.

Formula

\text{P(n, r)} = \frac{n!}{(n - r)!}

\text{C(n, r)} = \frac{n!}{r!(n - r)!}

Order

Order is important.Oder does not hold any relevance. 

Example

Arranging 3 books in a shelf.Choosing 3 books from a pile.
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