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 resource is interlinked so crawlers (and readers) can discover the next best action within a couple of clicks—one of the easiest ways to lift topical authority.
Deep dive & study plan
The Permutation Combination Calculator is a go-to tool whenever you need to computes npr, ncr, and factorial values exactly.. It focuses on permutation, combination, factorial, which means searchers often arrive with intent-heavy queries like “how to permutation combination calculator quickly” or “permutation combination calculator formula explained.” Use this calculator to capture those intents and keep learners on the page long enough to send positive engagement signals.
Under the hood, the calculator leans on big integers keep results exact even for large n (up to 300). outputs are displayed in standard or scientific notation depending on magnitude.—that’s why we surface the full expression (“nPr = n! / (n − r)! nCr = n! / (r! (n − r)!)”) directly above the interactive widget. When you embed that formula inside H2s or supporting paragraphs, you help both humans and crawlers understand what entity the page represents.
Execution matters as much as the math. Follow the built-in procedure: Step 1: Enter n (the total items) and r (items selected or arranged). Step 2: Review n!, nPr, and nCr instantly—values are exact integers. Step 3: Use the formatted result in proofs, probability setups, or combinatorics homework.. Each numbered instruction is short enough to scan on mobile but descriptive enough to satisfy Google’s Helpful Content guidelines. Encourage students to jot down units, double-check signs, and compare answers with the Example card to build confidence.
The Example section itself is packed with semantic clues: “n = 10, r = 4” leading to “10! = 3,628,800; 10P4 = 5,040; 10C4 = 210.” Pepper similar narratives throughout your copy (and internal links from related guides) so canonical search intents are answered without pogo-sticking back to Google.
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.
- Link out to at least two related calculators to keep readers exploring your topical hub.
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.