# Combination / Permutation Calculator

Number of objects | |

Total : | |

Choose : | |

Replacements : | |

Combinations : | |

Permutations : |

### Formulas

n | = | number of objects in total |

r | = | number of objects to choose |

### Combinations

\frac{n!}{r!(n-r)!}

### Combinations

With Replacements

\frac{(n+r-1)!}{r!(n-1)!}

### Permutations

\frac{n!}{(n-r)!}

### Permutations

With Replacements

n^r

## How do I use the Combination / Permutation calculator?

- Enter the total number of objects to choose from (
**Total)** - Enter the number of objects you want to choose (
**Choose)** **Choose**must be less than or equal to**Total**(≤)- Select whether replacements are allowed
- See the results appear instantly

## How to think about combinations and permutations

Let's use an example - choose 3 letters from the alphabet:

When counting **combinations**:

- [a, b, c] is the
as [c, b, a]__same combination__ - both represent the choice of letters a, b, and c. In any order.
*Order doesn't matter*.

When counting **permutations**:

- [a, b, c] is a
than [c, b, a]__different permutation__ - [a, b, c] represents the choice of a, then b, then c.
*In that particular order*. - [c, b, a] represents the choice of c, then b, then a.
*In that particular order*. *Order matters*.

**Summary**:

- A
**combination**refers to the*number of ways to choose*elements from a set,*in any order*. - A
**permutation**refers to the*number of ways to choose*elements from a set,*in a particular order*.