Permutation Calculator
Count ordered arrangements nPr exactly, even for very large numbers, using big-integer math.
Permutation Calculator
Count ordered arrangements nPr exactly, even for very large numbers, using big-integer math.
How to use the Permutation Calculator
- Enter n (total items to choose from).
- Enter r (items to arrange).
- Click Calculate.
Formula
P(n, r) = n! / (n − r)!
Example
P(10, 3) = 10! / 7! = 10 × 9 × 8 = 720
Step-by-step calculation
- n! / (n−r)! = 10!/7! = 10 × 9 × 8.
- Calculate: 10 × 9 = 90, 90 × 8 = 720.
- 720 ordered arrangements.
Real-world uses
- Combination lock possibilities.
- Race finishing order calculations.
- Arrangement optimization.
Common mistakes
- Confusing permutations with combinations.
- Using r > n (not possible).
- Forgetting that order matters in permutations.
Frequently asked questions
When does order matter?
Always in permutations. ABC is different from BAC.
What is nPr on a calculator?
P(n,r) is the number of ways to arrange r items selected from n.
How large can n and r be?
Up to 100,000 each. Results are calculated with exact big-integer arithmetic.