Combinatorics · Lesson
A sequence has k ordered positions. If each position may choose again among the same n symbols, the product principle gives n^k.
Prerequisites: Fundamental counting principle
Goal: Count length-k sequences when each position may reuse any of n symbols: n^k.
Change the data, observe how the number of cases changes, and use the lab to understand the counting structure you are using.
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Each position starts again with all n choices: multiply n by itself k times.
Data / situation: A code has 5 positions and each position can use one of 6 symbols, with repetition.
ConceptStep separates what is required from what is recommended or useful as reinforcement. Only required prerequisites block your progress.
Relationships: solid line = required · dashed line = recommended · dotted line = reinforcement.