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Combinations & Permutations

Calculate the number of combinations (nCr) and permutations (nPr) for probability and counting problems.

Our free Combinations & Permutations lets you calculate the number of combinations (nCr) and permutations (nPr) for probability and counting problems. It is built for students, teachers, engineers, and professionals who need fast, reliable math results who need fast, reliable results without installing software or creating an account.

Combinations & Permutations runs entirely in your browser on CalculatorsPlus — enter your values, get instant results, and copy or share your output in one click. Your data never leaves your device; we do not store inputs on any server.

Use the combinations & permutations to verify manual work, explore "what if" scenarios, and save time on repetitive calculations. For learning, try solving the problem by hand first, then check your answer here.

Results update in real time as you change inputs, so you can explore "what if" scenarios — adjust one variable at a time to see how it affects the outcome before committing to a purchase, plan, or decision.

This page includes step-by-step instructions, frequently asked questions, and practical tips below the calculator. Bookmark it for repeat use — many math tasks come up weekly during projects, studies, or financial planning.

Common Uses

  • ✓Homework verification and exam preparation
  • ✓Quick checks during work, shopping, or DIY projects
  • ✓Teaching demonstrations and classroom examples
  • ✓Engineering and spreadsheet formula validation

How to Use the Combinations & Permutations

  1. 1

    Enter n (total items)

    Input the total number of items in the set.

  2. 2

    Enter r (items chosen)

    Input how many items you are selecting.

  3. 3

    Choose type

    Select combination (order irrelevant) or permutation (order matters).

  4. 4

    View result

    See the number of possible combinations or permutations.

💡 Tips & Tricks

  • •Ask yourself: "Does the order of selection matter?" If yes, use permutations.
  • •Lottery calculations use combinations (order of drawn numbers does not matter).
  • •Password/PIN calculations use permutations (order matters).

Frequently Asked Questions

What is the difference between combinations and permutations?
Permutations: order matters (arrangements). Combinations: order does not matter (selections). Choosing 3 people for specific roles = permutation. Choosing 3 from a group = combination.
How do I calculate nCr?
nCr = n! / (r! × (n-r)!). Example: 10C3 = 10! / (3! × 7!) = 120 ways to choose 3 items from 10.
How do I calculate nPr?
nPr = n! / (n-r)!. Example: 10P3 = 10! / 7! = 720 ordered arrangements of 3 items from 10.
What is a factorial?
n! (n factorial) is the product of all positive integers up to n. Example: 5! = 5×4×3×2×1 = 120. By definition, 0! = 1.

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