Combinations & Permutations Calculator
Calculate permutations (nPr) and combinations (nCr) with step-by-step factorial computation. Includes repetition variants.
What is Combinations & Permutations Calculator?
This combinations and permutations calculator computes nCr (order does not matter) and nPr (order matters) with and without repetition allowed. Shows the complete factorial expansion and simplification for each calculation.
How to Use This Calculator
- Enter your Total outcomes (n), Choose (r), Favorable outcomes in the input fields provided
- Results are computed instantly as you enter or modify values — no need to click a button
- Review the computed output showing your combinations & permutations results with a detailed breakdown
- Cross-check the output with your manual working to reinforce the underlying concept
How Combinations & Permutations Calculator is Calculated
This calculator uses the formula: C(n,r) = n! / (r! × (n−r)!) | P(n,r) = n! / (n−r)!. Where n = Total items ; r = Items chosen ; Probability = Favorable / Total outcomes. Combinations ignore order (choosing), permutations consider order (arranging). All calculations run entirely in your browser — no data is transmitted to any server.
Frequently Asked Questions
When do I use combinations vs permutations?
Combinations (nCr): choosing a committee of 3 from 10 people — order does not matter. Permutations (nPr): selecting President, VP, and Secretary from 10 — order matters. nCr is always ≤ nPr.
What is nCr in simple terms?
nCr = n! / (r! × (n−r)!). It counts the number of ways to choose r items from n items. 10C3 = 10!/(3!×7!) = 120 ways to choose 3 from 10. Also written as "10 choose 3" or C(10,3).
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Why This Tool Is Essential
Accurate mathematical computation is the foundation of problem-solving across science, engineering, and everyday life. Combinations & Permutations Calculator provides instant, step-by-step solutions using validated algorithms. Whether you are a student preparing for JEE, NEET, or board exams, a professional verifying calculations, or a researcher needing quick computation, this tool eliminates manual errors and shows the complete solution methodology.
Key Features
- Instant Combinations & Permutations Calculator calculation with validated formulas
- Detailed step-by-step result breakdown
- Works offline as a Progressive Web App
- Completely free — no signup or data collection
- Mobile-friendly responsive design
- Save and share your results easily
Tips for Better Results
- 💡 Verify your understanding by working through the step-by-step solution shown.
- 💡 Practice with different values to build intuition about how the formula behaves.
- 💡 For competitive exams, learn the shortcuts alongside the standard method.
- 💡 Cross-verify with manual calculation for critical applications.
- 💡 Bookmark for quick access during study sessions — works offline too.
Ideal Users
Students preparing for JEE, NEET, and board exams, mathematics teachers creating worksheets, engineers and scientists needing quick computation, and anyone working with numbers.
📚 Complete Guide Available
Want to learn more? Read our comprehensive guide with detailed explanations, real-world examples, expert analysis, and actionable tips.
Read: CombinationsNote: This calculator provides results based on standard mathematical formulas. Always verify important calculations independently.
Maintained by: Sagar Sahni, Calc Labz | Review: formula checks, worked examples, and periodic updates
Need a correction? Contact us with the calculator name, your inputs, and the issue you found.
Last updated: April 2026