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nCr / nPr Calculator — Combinations, Permutations, Factorial

Exact nCr, nPr and n! with big-integer precision. Client-side, no signup.

Free No signup Client-side Privacy friendly Updated

How to use

  1. 1 Enter n (the total number of items) and r (how many are chosen).
  2. 2 Read nCr (combinations), nPr (permutations) and n! (factorial).
  3. 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 = 2

Output

C(5,2) = 10 · P(5,2) = 20

Common use cases

  1. 1

    Probability problems

    Count the ways to choose or arrange items when computing probabilities.

  2. 2

    Lottery & combinatorics

    Find how many combinations are possible for a draw or selection.

  3. 3

    Study & interviews

    Verify counting-problem answers with exact values.

Summary

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

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.

Compare

Permutation vs Combination

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