What is the Combinations Calculator?
Calculate combinations (nCr) and permutations (nPr) online for free. Enter n and r to get the count of ways to choose or arrange items, with factorial formulas and step-by-step work. Handles large results like C(52,5) using arbitrary-precision arithmetic. Runs entirely in your browser with no signup.
How to use the Combinations Calculator
- Choose Combinations (nCr) or Permutations (nPr).
- Enter n (total items) and r (chosen items).
- Click Calculate.
- Review the count, formula, and multiplication steps.
- Copy the result or the full summary.
Common use cases
- Finding C(10,3) = 120 for a statistics problem
- Counting C(52,5) = 2,598,960 possible poker hands
- Computing P(8,3) = 336 ordered arrangements
Frequently asked questions
- What is the difference between combinations and permutations?
- Combinations (nCr) count unordered selections — order does not matter. Permutations (nPr) count ordered arrangements — order matters.
- What is the combinations formula?
- C(n,r) = n! ÷ (r! × (n−r)!). For example, C(5,2) = 10 ways to choose 2 items from 5.
- When is C(n,r) zero?
- When r > n, there are no ways to choose more items than exist, so the result is 0.
- What is the maximum n?
- n can be up to 10,000. Very large combination values are computed with arbitrary-precision arithmetic.
