Permutation & Combination Calculator

Permutations A(n,m) and combinations C(n,m)

Quick Answer

Permutation & Combination Calculator: Permutations A(n,m) and combinations C(n,m). Permutation & Combination Calculator uses standard math formulas to compute accurate results instantly.

Order matters → permutation; only selection matters → combination; slots can repeat → n^r.

n（total）

r（chosen）

C(n,r) = n! / (r!(n−r)!)

Combination C(n,r)

2,598,960

C(52,5)2,598,960

A(52,5)311,875,200

Probability of one specific combo1 / 2,598,960

C(52,47)2,598,960

Step-by-step

1C(52,5) = C(52,5) by symmetry
2= (52 × 51 × 50 × 49 × 48) / (5 × 4 × 3 × 2 × 1)
3= 2,598,960

Pascal row: C(10, r)

r	0	1	2	3	4	5	6	7	8	9	10
C(10,r)	1	10	45	120	210	252	210	120	45	10	1

💡 Identities: C(n,r) = C(n,n−r); A(n,r) = C(n,r) × r!. Large results use exact integer arithmetic while safe (≥10¹⁵ shown in scientific notation).

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How to Use

Enter values or expressions: type directly into the Permutation & Combination Calculator — keyboard friendly.
Instant results: everything computes live as you type, no button needed.
Follow the steps: the result panel shows full working and formula substitution.
Copy or recompute: one-click copy; change any input to recalculate instantly.

Key Points

Permutation & Combination Calculator is a free online math tool — open and use, no sign-up.
All calculations run locally in your browser; your data never leaves the device.
Key capability: Permutations A(n,m) and combinations C(n,m).
Results come with formulas and reference tables so you can verify every number.

Formula & How It Works

Permutation & Combination Calculator formula

Permutation & Combination Calculator uses standard math formulas to compute accurate results instantly.

FAQ

How do I use the Permutation & Combination Calculator?

Open the page and fill in the input fields — results update automatically. Permutations A(n,m) and combinations C(n,m).

Are the results accurate?

Yes. All calculations use standard mathematical formulas and are verified for accuracy.

Is it free? Do I need to sign up?

Completely free. No registration, login or download required — just open and use.

Does it work on mobile?

Yes. The responsive design works on phones, tablets and desktops.

Is my data saved?

No. All calculations run locally in your browser. Nothing is uploaded or stored.

Related Guides

Source & Updates

Standard mathematical formulas. All logic verified. Last updated: 2025-07

Last updated: 2026-08-04

Formulas and content on this page are reviewed by the YiJianSuan team. For reference only — official sources prevail.

Cite this page: YiJianSuan. Permutation & Combination Calculator[EB/OL]. https://www.yijiansuan.com/en/c/math/permutation

Results provided by this tool are for reference only and do not constitute professional advice.