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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Pro Tip
License plate formats illustrate permutations with replacement: a plate with 3 letters + 3 digits has 26³ × 10³ = 17,576,000 combinations — enough for most states' vehicle fleets.
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Did You Know?
A standard combination lock (3 numbers, 0–39) actually uses permutations WITH replacement: 40³ = 64,000 combinations. A determined thief can try all combinations in about 4 hours manually.
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