Combinatorics
Permutation Combination Calculator
Evaluate permutations, combinations, and factorials using precise big-integer arithmetic—perfect for counting problems.
Calculate nPr and nCr along with n! using exact integer arithmetic.
Counting formulas
nPr = n! / (n − r)! nCr = n! / (r! (n − r)!)
Big integers keep results exact even for large n (up to 300). Outputs are displayed in standard or scientific notation depending on magnitude.
How to use
- Enter n (the total items) and r (items selected or arranged).
- Review n!, nPr, and nCr instantly—values are exact integers.
- Use the formatted result in proofs, probability setups, or combinatorics homework.
Example
Input: n = 10, r = 4
Output: 10! = 3,628,800; 10P4 = 5,040; 10C4 = 210
Student-friendly breakdown
This walkthrough emphasizes the most searched ideas for Permutation Combination Calculator: combination calculator, permutation calculator, factorial calculator, npr calculator. Start with the formula above, then follow the guided steps to double-check your work. For quick revision, highlight the givens, plug into the equation, and finish by verifying your units.
Need more support? Use the links below to open the long-form guide, browse additional examples, or hop into adjacent calculators within the same topic — each one is a quick way to double-check your work or handle a related question without starting from scratch.
Deep dive & study plan
Permutation Combination Calculator: Computes nPr, nCr, and factorial values exactly. It's built around permutation, combination, factorial, so you can go from a raw question to a checked answer without switching tools.
The math behind it: Big integers keep results exact even for large n (up to 300). Outputs are displayed in standard or scientific notation depending on magnitude. The core relationship is nPr = n! / (n − r)! nCr = n! / (r! (n − r)!), shown above the calculator so you can see exactly how your inputs turn into the result.
To use it well: (1) Enter n (the total items) and r (items selected or arranged). (2) Review n!, nPr, and nCr instantly—values are exact integers. (3) Use the formatted result in proofs, probability setups, or combinatorics homework. Keep your units consistent as you go, and re-run a case you already know the answer to — it's the fastest way to catch a typo before it throws off a result you're relying on.
Worked example: entering n = 10, r = 4 returns 10! = 3,628,800; 10P4 = 5,040; 10C4 = 210. Try swapping in your own numbers next, especially a case you're unsure about, before you use this for something that matters.
Quick retention checklist
- Speak the formula aloud (or annotate it) so the relationships stick.
- Write each step in your own words and compare with the numbered list above.
- Swap in new numbers for the Example to make sure the calculator (and your logic) handles edge cases.
- Check at least one related calculator below — it's the fastest way to confirm your numbers still line up from a different angle.
FAQ & notes
What if r > n?
Permutations and combinations are undefined when r exceeds n, so the calculator prompts you to adjust the inputs.
How large can n be?
Values up to n = 300 are supported. Beyond that, factorials exceed the safe range for display and may be unwieldy.
What formula does the Permutation Combination Calculator use?
Big integers keep results exact even for large n (up to 300). Outputs are displayed in standard or scientific notation depending on magnitude.
How do I use the Permutation Combination Calculator?
Enter n (the total items) and r (items selected or arranged). Review n!, nPr, and nCr instantly—values are exact integers. Use the formatted result in proofs, probability setups, or combinatorics homework.