Combinatorics · Lesson
Choose only k elements from n, but positions are different: first-second-third is not the same selection in another order.
Prerequisites: Simple permutations
Goal: Count ordered selections of k distinct elements chosen from n using D(n,k)=n!/(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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Do not expand all of n!: stop after k factors, because the rest cancels with (n−k)!.
Data / situation: Among 9 finalists assign 4 ordered positions.
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.