Permutation & Combination Calculator

Calculate permutations (nPr) and combinations (nCr) with step-by-step breakdowns. Free online probability calculator.

About Permutation & Combination Calculator

Our Permutation & Combination Calculator computes both nPr (ordered arrangements) and nCr (unordered selections) with full factorial breakdowns. Perfect for probability, statistics, and combinatorics.

Permutation & Combination Calculator

Total Items (n) ?Total number of items to choose from

Items to Arrange (r) ?Number of items to select and arrange (r ≤ n)

Total Items (n) ?Total number of items to choose from

Items to Choose (r) ?Number of items to select (r ≤ n)

Permutation (nPr)

Combination (nCr)

Calculation Breakdown

n (total) --

r (selected) --

n! --

r! --

(n − r)! --

nPr = n! / (n−r)! --

nCr = n! / (r!(n−r)!) --

Key Differences

Permutation Order matters

Combination Order doesn't matter

Relation nPr = nCr × r!

Understanding Permutations & Combinations

Permutations count arrangements where order matters (e.g., lock codes). Combinations count selections where order doesn't matter (e.g., lottery picks).

Formulas

Permutation P(n,r) = n! / (n − r)! — ordered arrangements

Combination C(n,r) = n! / (r! × (n − r)!) — unordered selections

Factorial n! = n × (n−1) × (n−2) × ... × 2 × 1

Real-Life Examples

Lottery

6/49 Lottery: Choosing 6 numbers from 49 — C(49,6) = 13,983,816 combinations.

Password

4-digit PIN: 10 digits, 4 positions with repetition — 10^4 = 10,000 permutations.

Committee

Pick 3 from 10: Choosing a committee of 3 from 10 people — C(10,3) = 120.

Racing

Top 3 from 8: Medal positions — P(8,3) = 8 × 7 × 6 = 336 arrangements.

Disclaimer: Results are for general educational purposes only. Please verify important calculations independently.

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Features

Security

Secure & Private

Your files are processed securely and deleted immediately after.

Speed

Fast Processing

Get your results in seconds with our optimized processing engine.

Setup

No Installation

Works entirely in your browser. No software to install.

Pricing

Free to Use

Use this tool completely free with no hidden charges.

Limit

Generous Limits

Enjoy generous file limits with no surprise caps on size or count.

Quality

High Quality Output

Results are rendered at full quality, ready for production use.

Frequently Asked Questions

Is Permutation & Combination Calculator free to use?

Yes, this tool is completely free to use. There are no hidden fees or subscription requirements.

Are my files safe and secure?

Absolutely. All file processing happens securely. Your files are automatically deleted from our servers after processing.

What file formats are supported?

This tool supports a wide range of common file formats. Check the upload area for specific format requirements.

Do I need to create an account?

No account is required. Simply upload your file, process it, and download the result.

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Permutation & Combination Calculator

About Permutation & Combination Calculator

Permutation & Combination Calculator

Calculation Breakdown

Key Differences

Understanding Permutations & Combinations

Real-Life Examples

Warning

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Features

Secure & Private

Fast Processing

No Installation

Free to Use

Generous Limits

High Quality Output

Frequently Asked Questions

Rate This Tool

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