Permutation and Combination Calculator
Adjust the inputs below. Results update as you type.
How it works
Permutation (order matters): P(n,r) = n! / (n−r)!. Combination (order doesn't matter): C(n,r) = n! / (r!(n−r)!). Example: from 10 people, choose a president and VP = P(10,2) = 90; choose a 2-person committee = C(10,2) = 45. Pascal's Triangle rows give combinations. Used in probability, lottery odds, and algorithm complexity analysis.
Input guidance
- Check units and decimal placement before running calculations.
- For percentage and ratio tasks, define the baseline value clearly.
- Use rounded output carefully and keep full precision for intermediate steps.
The formula
Permutations (order matters): P(n,r) = n! ÷ (n−r)!. Combinations (order doesn't matter): C(n,r) = n! ÷ (r!(n−r)!).
Worked example
Choosing 3 of 5 items: permutations P(5,3) = 60, combinations C(5,3) = 10.
More examples to test
- Baseline example: solve with clean numbers first to verify formula direction.
- Edge-case example: test near-zero or boundary values to avoid interpretation errors.
How to interpret results
Use outputs as quick checks, then verify with step-by-step work for graded or high-stakes use.
When this can be inaccurate
Errors usually come from unit mismatch, wrong baseline assumptions, or rounding too early in multistep problems.
Change history
- July 2026: Quality-reviewed for publication with formula checks and explanatory copy updates.
Site-wide corrections also appear on the corrections log.
Build math and logic skills with guided lessons
Educational platform recommendation.
Frequently asked questions
What is the difference between permutation and combination?+
Permutations count ordered arrangements; combinations count unordered selections. ABC and CAB are one combination but two permutations.
What is a factorial?+
n! is the product of all positive integers up to n. 5! = 5×4×3×2×1 = 120. By definition, 0! = 1.
When do I use each?+
Use permutations when arrangement or sequence matters (passwords, rankings); use combinations when only the group matters (lottery picks, committees).
Why do my classroom and calculator results differ?+
Differences usually come from rounding conventions, order-of-operations handling, or different baseline assumptions.
What is the safest way to validate an answer?+
Recompute with units shown and check against a second method or manual arithmetic for critical problems.