Permutation Calculator
Count permutations P(n, r) — ordered arrangements — with or without repetition, exactly for large values.
Your inputs
Results
Permutations P(n, r)
720
- Number of digits
- 3
✓Exact calculation — rounded only for display
What this calculator does
Permutations count arrangements where order matters, such as rankings or PIN codes.
Formula and method
Without repetition: P(n, r) = n! ÷ (n − r)!; with repetition: n^r
Worked example
Calculated by this tool with its default inputs:
Inputs
- Total items (n): 10
- Items chosen (r): 3
- Repetition allowed: No
Results
- Permutations P(n, r): 720
- Number of digits: 3
How to read the results
Large results are exact big integers.
Assumptions and limitations
- r cannot exceed n without repetition.
Questions
How many 4-digit PINs are there?
10⁴ = 10,000, with repetition allowed.
Methodology and verification
- Result type
- Exact mathematical calculation (rounded only for display)
- Formula version
- 1.0
- Automated verification
- 3 reference and validation test cases, checked against independently computed values. The site cannot be built if any of them fail.
- Editorial review
- Awaiting human editorial review. The explanation was drafted with AI assistance; the formula and examples are verified by the automated tests above.
Privacy
Everything you enter is calculated in this browser and is not sent to Numerith or anyone else. Inputs are added to a share link only if you choose to include them. Privacy policy