combinations

Combinations with Repetition: Stars and Bars

2026-07-21·2468 words·12 mins

Discrete Mathematics combinatorics combinations

At an ice cream shop with 7 flavors, there are 210 ways to order 4 scoops, repeating flavors allowed. We get there with the stars and bars method, which shows that choosing with repetition, distributing balls into boxes, and solving integer equations are the same problem.

Combinations: When Order Does Not Matter

2026-07-09·1984 words·10 mins

Discrete Mathematics combinatorics combinations

Out of 10 friends, 3 go buy the popcorn. Only who goes matters, not the order of the choice, so there are 120 possible groups. We will see the combination formula, its symmetry, the complement method, and how to split a set into groups.

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