Combinations & Permutations
Calculate nCr and nPr with a visual showing selected vs. total arrangements
About this calculator
The Combinations and Permutations Calculator computes C(n,r) and P(n,r) for any n and r, showing both formulas and results side by side. Combinations count selections where order doesn't matter; permutations count arrangements where order does matter. Ideal for probability, statistics, and combinatorics problems.
How to use the Combinations & Permutations calculator
- Enter the values for your problem into the input fields.
- Read the result — it updates instantly as you type.
- Check the formula and the visual explanation to follow how the answer was found.
- Copy the page URL to share the exact calculation.
Common examples
- C(10, 3) = 120 combinations (choosing 3 from 10, order doesn't matter)
- P(10, 3) = 720 permutations (arranging 3 from 10, order matters)
- C(52, 5) = 2,598,960 — 5-card poker hand combinations
- P(5, 5) = 120 — ways to arrange 5 people in 5 seats
- C(6, 2) = 15 combinations vs P(6, 2) = 30 permutations
Frequently asked questions
How does the Combinations & Permutations calculator work?
Enter your values and the calculator applies the exact mathematical method for this problem, showing the result together with the formula it used. Everything is computed with high-precision arithmetic, so the answer you see is not limited by ordinary floating-point rounding.
When would I use the Combinations & Permutations calculator?
It is useful for homework and exam preparation, for checking work done by hand, and whenever a step in a larger problem needs this calculation done quickly and reliably.
How accurate are the results?
Calculations run at 30 significant digits of precision internally. Displayed values are rounded for readability, but the underlying result is far more precise than a typical hand or pocket-calculator computation.
Can I share a specific calculation with someone else?
Yes. Every value you enter updates the URL, so copying the address bar and sharing the link reopens the exact same calculation for whoever clicks it.