Permutations with Repetition

Combinatorics · Axiom Academy

LESSON Permutations with Repetition Understanding how to count ordered arrangements when items can be repeated Scenario: You are choosing r items from n types, where order matters and repetition is allowed . Think of it like creating a PIN code: each position can be any digit from 0-9, and you can use the same digit multiple times. Since each of the r positions can be filled in n ways independently, we multiply: Position 1: n choices × Position 2: n choices × ... × Position r: n choices Example: A 4-digit PIN code using digits 0-9 • Total PIN codes = 10^4 = 10,000 Permutations with repetition appear frequently in everyday situations: DNA Sequences: A DNA segment of length 5 • Total sequences = 4^5 = 1,024 License Plates: Format: 3 letters followed by 3 digits • Total combinations = 17,576 × 1,000 = 17,576,000 4. Contrast: With vs Without Repetition Understanding the difference between these two scenarios is crucial: The Key Difference: Without repetition, available choices decrease with each selection. With repetition, all choices remain available.

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