About this calculator
Results are exact for large numbers, and very long answers are shown in scientific notation with the digit count.
How to use it
- Enter n and r.
- Choose whether repetition is allowed.
- Read the number of arrangements.
The formula
nPr = n! ÷ (n − r)!; with repetition: nʳ
- n
- items available
- r
- items arranged
Worked example
Gold, silver and bronze among 10 runners
- 10P3 = 10 × 9 × 8 = 720.
What the result means
With repetition each place can be any item: a 4-digit PIN has 10⁴ = 10,000 possibilities.
Assumptions
- Items are distinct.
Limitations
- n up to 1,00,000 and r up to 20,000.
Frequently asked questions
What is the difference between permutation and combination?
Permutations count arrangements, where order matters. Combinations count selections, where order does not. ABC and CBA are two permutations but one combination.
What is 0!?
1, by definition. So nP0 = nC0 = 1.
How many ways can 5 people sit in a row?
5P5 = 5! = 120.
Last reviewed on 6 October 2026. Found a mistake? Tell us.