nCr / nPr Calculator — Combinations, Permutations, Factorial
Exact nCr, nPr and n! with big-integer precision. Client-side, no signup.
Combinations nCr
order doesn't matter
Permutations nPr
order matters
Factorial n!
Enter non-negative integers for n and r.
How to use
- 1 Enter n (the total number of items) and r (how many are chosen).
- 2 Read nCr (combinations), nPr (permutations) and n! (factorial).
- 3 Big results are computed exactly with BigInt — no rounding.
Why use this tool
- Exact combinations, permutations and factorials, even for large n.
- Clear reminder of when order matters (permutations) vs not (combinations).
- Runs entirely in your browser.
Frequently asked questions
What is the difference between nCr and nPr?
Permutations (nPr) count ordered arrangements; combinations (nCr) count unordered selections. nPr = n!/(n−r)!, nCr = n!/(r!(n−r)!).
What is a factorial?
n! is the product of all positive integers up to n: 5! = 5×4×3×2×1 = 120. By definition 0! = 1.
Why is there a limit on n!?
Factorials grow extremely fast; the factorial display is capped at n ≤ 1000 to keep the output readable. nCr/nPr still work for any r ≤ n.
Are the results exact?
Yes — they use arbitrary-precision BigInt arithmetic, so even huge values are exact.
What is Combinations & Permutations Calculator?
A combinatorics calculator computes the number of combinations (nCr), permutations (nPr), and the factorial (n!) for given values of n and r, using exact arbitrary-precision arithmetic.
Features
nCr and nPr
Combinations (order-independent) and permutations (order-dependent) computed together.
Exact big integers
Uses BigInt, so results for large n and r are exact, not floating-point approximations.
Free & private
Runs on your device — nothing is uploaded.
Example
Input
n = 5, r = 2Output
C(5,2) = 10 · P(5,2) = 20Common use cases
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1
Probability problems
Count the ways to choose or arrange items when computing probabilities.
-
2
Lottery & combinatorics
Find how many combinations are possible for a draw or selection.
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3
Study & interviews
Verify counting-problem answers with exact values.
Zerethon's combinations & permutations calculator computes nCr (combinations) and nPr (permutations) for given n and r in your browser, using exact BigInt arithmetic so large values don't lose precision. Everything runs client-side — nothing is uploaded.
- Category
- Math
- Pricing
- Free
- Privacy
- Browser-based
- Signup
- Not required
References
- Combination — Wolfram MathWorld — Wolfram MathWorld
- Permutation — Wolfram MathWorld — Wolfram MathWorld
Privacy
Your data never leaves your browser unless explicitly stated. Combinations & Permutations Calculator runs entirely client-side — no server upload, no logging, no tracking of your input.
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