How to Calculate Permutations with Replacement
What is Permutations with Replacement?
Permutations with replacement count ordered arrangements where items can be repeated. Formula: n^k (n choices, k selections). Used in PIN codes, passwords, combination locks, and license plates.
Step-by-Step Guide
- 1Order matters AND repetition allowed
- 2Total = n^k (n choices for each of k positions)
- 3Example: 4-digit PIN with digits 0-9: 10^4 = 10,000 possible PINs
- 4Contrast: permutations without replacement = n!/(n-k)!
Worked Examples
Input
3-letter code from 26 letters, repeats allowed
Result
26³ = 17,576 codes
Input
4-digit PIN (0–9)
Result
10⁴ = 10,000 PINs
Without replacement: 10×9×8×7 = 5,040
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