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Kordu Tools
Math & Numbers Runs in browser Updated 30 Mar 2026

Permutation & Combination Calculator

Calculate nPr permutations and nCr combinations with step-by-step formula breakdowns. Supports with and without repetition. BigInt precision.

r must be less than or equal to n when repetition is disabled.

n must be a positive integer (1 to 1,000).

r must be a non-negative integer (0 to 1,000).

Permutations (nPr)

Order matters

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Combinations (nCr)

Order does not matter

—

Step-by-Step Breakdown

Permutation

—

—

= —

Combination

—

—

= —

n!—
r!—
(n-r)!—

Enter n and r above to calculate permutations and combinations.

Formulae

nPr = n! / (n−r)!   (without repetition)

nPr = n^r   (with repetition)

nCr = n! / (r!(n−r)!)   (without repetition)

nCr = (n+r−1)! / (r!(n−1)!)   (with repetition)
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How to use Permutation & Combination Calculator

  1. Enter n (total items)

    Type the total number of items in the set. For example, the number of players to choose from.

  2. Enter r (items to choose)

    Type how many items you are selecting or arranging. Must be ≤ n.

  3. View nPr and nCr simultaneously

    Both permutation and combination values appear instantly with formula expansions below.

  4. Toggle repetition mode

    Enable 'With Repetition' to calculate arrangements and selections where items can be chosen more than once.

  5. Read the step-by-step working

    Expand the working to see how factorials are applied at each stage of the calculation.

Permutation & Combination Calculator FAQ

What is the difference between permutation and combination?
Permutations count ordered arrangements — ABC and BAC are different. Combinations count unordered selections — ABC and BAC are the same. Use permutations when order matters, combinations when it doesn't.

What is the formula for permutations (nPr)?
nPr = n! / (n−r)! where n is total items and r is items chosen. Example: 4P2 = 4!/(4−2)! = 24/2 = 12.

What is the formula for combinations (nCr)?
nCr = n! / (r! × (n−r)!). Example: 4C2 = 4!/(2! × 2!) = 24/(2×2) = 6.

What does 'with repetition' mean?
Items can be chosen more than once. Permutations with repetition = n^r. Combinations with repetition = (n+r−1)! / (r! × (n−1)!).

When do I use combinations vs permutations?
Use combinations for: choosing a team, selecting lottery numbers, picking pizza toppings. Use permutations for: race standings, password arrangements, seating order.

How is this related to probability?
Probability of an event = favorable outcomes / total outcomes. Combinations and permutations calculate those counts.

What is 10C3?
10C3 = 10! / (3! × 7!) = 120. This is the number of ways to choose 3 items from 10 when order doesn't matter.

How large can n and r be?
The tool uses BigInt for exact results, supporting very large factorials without floating-point rounding errors.

Can I use this for homework?
Yes. The step-by-step formula expansion shows every stage of the calculation so you can verify your method.

Is any data sent to a server?
No. All calculations run entirely in your browser. Nothing is uploaded or stored.

Background

Calculate permutations and combinations for any values of n and r. Both nPr (ordered arrangements) and nCr (unordered selections) are computed simultaneously and displayed side by side with a step-by-step formula expansion — ideal for verifying homework or understanding the difference between the two. Repetition mode switches to the formulas for arrangements and selections where items can be reused. BigInt arithmetic provides exact results even for large factorials. Common applications include counting lottery combinations, password strength estimation, seating arrangements, genetics, probability problems, and combinatorics coursework. The tool explains which formula applies to your problem and why, making it educational as well as functional. All processing runs in your browser with no data uploaded.

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