Permutation with Repetition Calculator
Enter the number of distinct options n and positions k to calculate nᵏ, the number of ordered arrangements when items may repeat.
Permutations with repetition: 1,296
Instructions
- Enter the number of distinct choices (n).
- Enter the length of each ordered selection (k).
- Review nᵏ, the count of permutations with repetition.
- Apply to password counting, PIN codes, or arrangement problems where repeats are allowed.
Formula
Permutations with repetition = nᵏ
Special case: if k = 0, nᵏ = 1 (empty arrangement)
Works for integers n ≥ 0 and k ≥ 0
About This Tool
Permutations with repetition model scenarios where each position can be filled independently from the same set of choices. Common examples include PIN codes, character strings, and arrangements in combinatorial counting where order matters and repeats are allowed.
Common Questions
What if k = 0?
There is exactly one arrangement: the empty tuple. The calculator reports 1.
Can n be zero?
If n = 0 and k > 0, no arrangements exist. The calculator returns zero.
How is this different from permutations without repetition?
Without repetition, each option can be used at most once and the formula is n! / (n − k)!. Here, repetitions are allowed, so the count is nᵏ.
Does the order matter?
Yes. Permutations count ordered arrangements. Change the order and you have a different permutation.