Combinatorics · Lesson
When choosing k objects from n types, a type may repeat and order does not matter. Stars and bars transforms the problem into a simple combination.
Prerequisites: Simple combinations
Goal: Count unordered selections with repetition using stars and bars and C(n+k-1,k).
Change the data, observe how the number of cases changes, and use the lab to understand the counting structure you are using.
Loading laboratory…
Completed exercises: 0/5 · Correct on first attempt: 0
With k stars and n−1 bars there are n+k−1 symbols in total; choose where the k stars go (or equivalently the bars).
Data / situation: Choose 3 scoops from 5 flavours; flavours may repeat and order does not matter.
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.