Combinatorics Calculator
Calculate exact permutations and combinations with or without repetition from a simple n, r, and mode input.
Last updated: 2026-03-27
Combinatorics calculator
Enter your values
Enter n, r, and the counting mode to calculate an exact permutation or combination count.
Exact Count
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Enter total items, chosen items, and the counting mode to get the exact count and formula.
Calculation History(0)
Example calculations
Tap an example to prefill the calculator with sample values.
Lottery-style combination
Choose 6 numbers from 49
An unordered selection without repetition is the classic combination example.
Result: The exact count is huge because the search space grows quickly even without order
4-digit passcode
10 digits with repetition allowed
Ordered selections with repetition model most simple PIN or code-style counts.
Result: Order matters, so the count is much larger than a combination case
How the counting mode changes the answer
The key choice is whether order matters and whether the same item can be selected more than once. That decision determines which formula belongs to the problem.
The calculator keeps the arithmetic exact with bigint math so large but reasonable classroom-scale counts do not collapse into floating-point approximations.
Combinatorics calculator FAQs
Use the mode selector to separate order-sensitive problems from grouping problems.
What is the difference between permutations and combinations?
Permutations care about order, while combinations do not. If swapping two chosen items creates a new outcome, you are usually working with permutations.
What does repetition mean here?
Repetition means the same source item can be chosen more than once. Password digits are a common ordered-with-repetition example, while ice-cream scoops are a common unordered-with-repetition example.
Why do the numbers get huge so quickly?
Because each extra item or position multiplies the search space. Combinatorics grows fast, which is why exact integer handling matters even for medium-sized classroom problems.
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Pair counting problems with neighboring statistics and probability tools.
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