Permutation & Combination Calculator
Calculate permutations (nPr) and combinations (nCr) for given n and r, with factorial safety limits.
Last reviewed by the Radiatus Cloud team
Output
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Calculate permutations and combinations
Counting how many ways things can be arranged or chosen is core to probability and statistics, and the two operations, permutations and combinations, are easy to confuse. This calculator computes both nPr and nCr for given values, with the factorials shown, so you get the right count and see how it is derived.
The difference that matters
The key distinction is whether order matters. A permutation counts arrangements where order matters, first, second and third place in a race, while a combination counts selections where it does not, three people chosen for a committee. Using the wrong one is the classic mistake, and it gives an answer off by a factor of the arrangements. The calculator computes both so you can pick the right one, and showing the factorials makes the formula concrete rather than a black box.
The right count, shown
Everything runs in your browser, so nothing you enter is uploaded and the tool works without an account. That keeps your study material and notes private on your own machine while you learn.
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Frequently Asked Questions
What is the difference between nPr and nCr?
A permutation (nPr) counts arrangements where order matters; a combination (nCr) counts selections where order does not. Choosing the wrong one is the classic error.
When does order matter?
When the positions are distinct, like first, second and third in a race, use permutations. When only the group matters, like people chosen for a committee, use combinations.
Why show the factorials?
Because seeing the factorial terms makes the formula concrete and helps you understand how the count is derived rather than treating it as a black box.
What are these used for?
Probability, statistics and combinatorics, wherever you need to count the ways things can be arranged or selected.
Is my input uploaded?
No. The calculation runs entirely in your browser.
Privacy & Security
Calculated locally in your browser. No data is sent to any server.
How to Use
Enter n and r to compute nPr and nCr.
Disclaimer: This tool is provided "as is" without warranty of any kind. Results are for educational and utility purposes.