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 same combination as [c, b, a]
- 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 different permutation than [c, b, a]
- [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.