Permutation without Repetition Calculator
Enter total items n and selection size k to compute P(n, k) = n! / (n − k)! — the number of ways to arrange k distinct items.
P(n, k): 5,040
How to Use This Calculator
- Enter total distinct items n.
- Enter how many items are arranged (k).
- Read the number of permutations without repetition.
- Use results in probability, counting, or scheduling problems.
Formula
P(n, k) = n! / (n − k)!
Recursive: P(n, k) = n × P(n − 1, k − 1)
Defined for integers with 0 ≤ k ≤ n
Full Description
Permutations without repetition count ordered selections of distinct items. They appear in ranking problems, password counting (without repeated characters), and arrangement of objects when order matters.
Frequently Asked Questions
What if k = n?
P(n, n) = n!, counting all possible orderings of n distinct items.
Can k exceed n?
No. Selecting more items than available isn’t defined; the calculator limits k to n.
Is repetition allowed?
Not here. Use the permutations with repetition calculator for scenarios permitting repeated selections.
Do I need factorials?
The tool handles factorial calculations internally via multiplicative formulas to avoid overflow.