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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.

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1. 1Order matters AND repetition allowed
2. 2Total = n^k (n choices for each of k positions)
3. 3Example: 4-digit PIN with digits 0-9: 10^4 = 10,000 possible PINs
4. 4Contrast: permutations without replacement = n!/(n-k)!

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