# Difference between Permutation and Combination

May 13, 2023

Permutation involves arranging a set of objects in a particular order, while combination involves selecting a subset of objects from a larger set without regard to order.

**Permutation Vs Combination**

Permutation | Combination |

Order matters and the arrangement of members is important | Order matters, and the arrangement of members is important |

n! / (n-r)! | n! / r!(n-r)! |

nPr or P(n,r) | nCr or C(n,r) |

Arranging 4 books on a shelf in different orders | Selecting 4 books from a shelf without considering their order |

nPr = n! / (n-r)! where n is the total number of objects and r is the number of objects selected | nCr = n! / r!(n-r)! where n is the total number of objects and r is the number of objects selected |

**4 Difference between Permutation and Combination**

- Permutation considers the order of elements, while combination does not.
- A permutation is used when the arrangement or order of elements is important, while a combination is used when only the selection of elements matters.
- The permutation is denoted as nPr or P(n,r), while the combination is denoted as nCr or C(n,r).
- The formula for permutation is n! / (n-r)!, while the formula for combination is n! / r!(n-r)!.

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