Permutations and Combinations
Count nPr, nCr and their repetition variants.
How to use
- 1 Enter n, the total number of items available.
- 2 Enter r, how many you are choosing or arranging.
- 3 Read the four results: nPr, nCr and both repetition variants.
- 4 Use permutations when order matters and combinations when it does not.
- 5 Copy the results if you need them.
About Permutations and Combinations
The Permutations and Combinations calculator answers the everyday counting question "how many ways can I arrange or choose things?" for any two whole numbers n and r.
It computes four quantities at once.
Permutations without repetition, written nPr, count the ordered selections of r items from n distinct items — useful when order matters, such as the number of possible podium finishes in a race.
Combinations without repetition, written nCr, count the unordered selections — the right tool when order does not matter, like picking a committee or a lottery draw.
The calculator also covers the with-repetition cases: n raised to the power r counts ordered selections where the same item may be reused (think digits in a PIN), and the multiset coefficient C(n + r − 1, r) counts unordered selections with repetition allowed (think scoops of ice cream chosen from a fixed set of flavours).
Because these numbers grow explosively — 52 choose 5 is already nearly 2.6 million and full factorials overflow ordinary floating point — every result is computed with arbitrary-precision BigInt arithmetic and shown as an exact decimal string, never a rounded approximation.
The combination routines multiply incrementally so even large inputs stay fast and precise.
Everything runs locally in your browser, so nothing you enter is uploaded, logged or stored, and the calculator keeps working offline once the page has loaded.
FAQ
What is the difference between a permutation and a combination?
A permutation counts arrangements where order matters, so ABC and CBA are different. A combination counts selections where order does not matter, so ABC and CBA are the same choice.
What do the "with repetition" results mean?
They allow the same item to be picked more than once. n^r counts ordered picks with repetition (like a PIN), and C(n+r-1, r) counts unordered picks with repetition (like choosing scoops of ice cream).
Are the results exact for large numbers?
Yes. All calculations use arbitrary-precision BigInt arithmetic, so even huge values are returned as exact decimal strings with no floating-point rounding.