How to use the Permutation & Combination Calculator
- Enter the total number of items n.
- Enter how many you choose, r.
- Tick “items can repeat” if the same item can be picked again.
What does this tool do?
Permutations count ordered arrangements: picking a president, secretary and treasurer from 10 people is P(10, 3) = 720. Combinations ignore order: choosing any 3 people for a committee is C(10, 3) = 120.
With repetition, a 4-digit PIN from 10 digits has 10⁴ = 10,000 permutations. Combinations with repetition — like picking 3 scoops from 10 flavours where repeats are allowed — use C(n + r − 1, r).
Why use it?
- Both answers at once.
- Handles repetition.
- Exact big-number arithmetic.
The formula
P(n, r) = n! ÷ (n − r)!
C(n, r) = n! ÷ (r! (n − r)!)
With repetition: nʳ and C(n + r − 1, r)
Privacy
The calculation happens instantly in your browser. The numbers you enter are not sent to our servers or saved. There's no account to create and nothing to install.
Frequently asked questions
How do I know whether order matters?
If swapping two chosen items gives a different outcome (positions, rankings, codes), use permutations. If it's the same group, use combinations.
Last reviewed by the M2Toolkit team.