Combinatorics · Lesson
If you choose a group and the order of names does not change the group, the k! internal permutations must be counted only once.
Prerequisites: Simple arrangements and factorial
Goal: Count groups of k elements chosen from n when order does not matter using the binomial coefficient.
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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Start from arrangements and divide by k!: each group was counted once for every internal order.
Data / situation: Choose a team of 2 from 12 students.
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.