Enter whole numbers n and r with 0 ≤ r ≤ n.
Combinatorics Calculator
Factorial, Permutation & Combination Calculator
Calculate n factorial, ordered arrangements nPr, and unordered selections nCr for whole-number inputs.
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Use the example values or replace them with your own. Required validation happens before the calculation.
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Simple workflow
How to use the Factorial, Permutation & Combination Calculator
Follow these steps to get a reliable result and understand how it was produced.
Calculate n! and the reduced factorial ratios.
Compare ordered permutations with unordered combinations.
Understanding the calculation
Permutations count arrangements where order matters. Combinations count selections where order does not matter.
nPr = n!/(n−r)!; nCr = n!/[r!(n−r)!]The result panel substitutes your numbers into this relationship and shows the important intermediate values.
Common uses
- Probability counting
- Team and committee selection
- Arrangement and scheduling problems
Accuracy tips
- Order matters for permutations but not combinations.
- 0! equals 1.
- Browser numbers overflow beyond about 170!; practical limits are enforced.
Helpful answers
Factorial, Permutation & Combination Calculator FAQs
Important details about formulas, inputs, limitations, and result interpretation.
What is a factorial?
n! is the product of all positive integers from n down to 1, with 0!=1.
When should I use nPr?
Use permutations when different orders count as different outcomes.
When should I use nCr?
Use combinations when only the selected group matters, not its order.
Why must r be no greater than n?
You cannot select or arrange more distinct items than are available.