A permutation is for lists where does order matters but in Combination, it doesn’t. Practically, both involve selecting a subset from several elements.

With a simple example, when you return from the market, if your mom asks about the price, you should say it 235 (which is actual), not 325 or 532. That’s Permutation.

## Key Takeaways

- A permutation is an arrangement of objects in a specific order, with the number of permutations calculated as the total possible orderings of those objects.
- A combination is a selection of objects without regard to their order. The number of combinations is calculated as the possible ways to choose a specific number of objects from a larger set.
- Both permutations and combinations are concepts in combinatorics, but they differ in whether the order of objects matters, with permutations, focused on ordered arrangements and combinations on unordered selections.

**Permutation vs Combination**

The difference between Permutation and Combination is that in a permutation, the order of the elements is taken into consideration and a permutation can be either with repetition or without repetition. In a combination, the order of the elements is not a matter of concern.

## Comparison Table

Parameter of comparison | Permutation | Combination |
---|---|---|

Definition | ‘Permutation’ is a collection of an object where the order of objects is important. | ‘Combination’ is a collection of objects where an order isn’t important. |

Represents | Arrangement | Selection |

Order effects | Yes | No |

Derived | Multiple Permutation derived from a single combination | Only single Combination may be derived from a Permutation |

## What is Permutation?

*‘Permutation’* is defined as an arrangement that can be done using some of the objects or items in an ordered manner. It’s all about arrangement.

Suppose, a smartphone is locked by a PIN code which is 9396. To unlock, it won’t open if you enter 9693, because there is a different ordering for your smartphone’s PIN.

## What is Combination?

*‘Combination’*** **is defined as the selection that can be done using some of the items where order does not matter.

**Main Differences Between Permutation and Combination**

The difference Between Permutation and Combination are clearly explained below:

- Placement and order is the main difference between permutation and combination. In permutation, we are restricted to comply with an order but in combination, there is no such restriction.
- A permutation is just an arrangement of the things where the arrangement will be in a specific order. The combination is a selection where the selection is without any specific order.
- In Permutation, the number of arrangements is denoted by nPr.
- Multiple permutations can be derived from a single combination but only a single combination may be derived from one permutation.
- A permutation is the choice of ‘r’ things from the group or set of ‘n’ things with the order. The combination is a selection of ‘r’ things from the large set or group of ‘n’ things without any specific order.

**References**

- https://pubs.acs.org/doi/abs/10.1021/co300148c
- https://onlinelibrary.wiley.com/doi/abs/10.1002/asmb.1976

Last Updated : 11 June, 2023

Emma Smith holds an MA degree in English from Irvine Valley College. She has been a Journalist since 2002, writing articles on the English language, Sports, and Law. Read more about me on her bio page.

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