Permutation and Combination Calculator — Rex's Toolbox

Rex says

The fast lane for the math you almost remember from school. Type the numbers, get the answer, move on with your day.

Try a scenario

Click to load — tweak from there.

Inputs

n (total items)

r (chosen)

Result

Combinations (nCr)

2,598,960

Permutations (nPr)

311,875,200

Arrangements with repetition (nʳ)

380,204,032

n factorial

80,658,175,170,943,880,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000

Odds of one specific combination

0.0000003848

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How to use this

1Enter n (total items).
2Enter r (chosen).
3Read your combinations (ncr) on the right — it updates as you type.
4Hit Share to keep the scenario or send it to someone.

About this calculator

Permutations count arrangements where order matters; combinations count selections where it does not. Lottery odds, team picks, and password strength all reduce to one of these two.

FormulanPr = n! ÷ (n−r)!. nCr = n! ÷ (r!(n−r)!).

Worked example

Using the values the calculator loads with:

Inputs

n (total items): 52
r (chosen): 5

Results

Combinations (nCr): 2,598,960
Permutations (nPr): 311,875,200
Arrangements with repetition (nʳ): 380,204,032
n factorial: 80,658,175,170,943,880,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000
Odds of one specific combination: 0.0000003848

What each field means

Inputs

n (total items): The n (total items) used in the calculation. Starts at 52 so you have a working example on load. Accepted range: 0–170.
r (chosen): The r (chosen) used in the calculation. Starts at 5 so you have a working example on load.

Results

Combinations (nCr): Returned as a whole number and shown as the headline result. It recalculates instantly whenever you change an input, so you can compare scenarios without reloading.
Permutations (nPr): Returned as a whole number. It recalculates instantly whenever you change an input, so you can compare scenarios without reloading.
Arrangements with repetition (nʳ): Returned as a whole number. It recalculates instantly whenever you change an input, so you can compare scenarios without reloading.
n factorial: Returned as a whole number. It recalculates instantly whenever you change an input, so you can compare scenarios without reloading.
Odds of one specific combination: Returned as a decimal number. It recalculates instantly whenever you change an input, so you can compare scenarios without reloading.

FAQ

How does the permutation and combination calculator work?

Permutations count arrangements where order matters; combinations count selections where it does not. Lottery odds, team picks, and password strength all reduce to one of these two. The underlying maths is: nPr = n! ÷ (n−r)!. nCr = n! ÷ (r!(n−r)!).

What do I need to enter?

2 values: n (total items), and r (chosen). Each field starts with a sensible default, so you can change one number at a time and watch the result move.

What does the combinations (ncr) result mean?

It is returned as a whole number and updates live as you edit the inputs, so you can compare two or three versions of a scenario in a few seconds.

Is this calculator free, and do I need an account?

Yes, it's free, and no account is required. Nothing you type is stored on our servers — the maths runs entirely in your browser.

How accurate is the result?

It applies the standard formula exactly, so the arithmetic is precise. Results are rounded for display; the underlying calculation keeps full precision.

Who is this tool for?

It's built for students, developers, and anyone who needs the answer right now without setting up a spreadsheet.

Accuracy and limitations

Results are rounded for display; the underlying calculation keeps full precision.
Very large or very small inputs may hit floating-point limits in the browser.
Inputs outside the accepted range are clamped rather than rejected.

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Cite this calculator

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APA

RevenueLab. (2026). Permutation and Combination Calculator. Retrieved from https://www.revenuelab.fyi/toolbox/permutation-combination

HTML

<p>Source: <a href="https://www.revenuelab.fyi/toolbox/permutation-combination" target="_blank" rel="noopener">Permutation and Combination Calculator — RevenueLab</a> (2026).</p>

Markdown

Source: [Permutation and Combination Calculator — RevenueLab](https://www.revenuelab.fyi/toolbox/permutation-combination) (2026).