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Math · Intermediate

Counting & Combinatorics

How many passwords? How many poker hands? How many ways to share out sweets? Learn the multiplication principle, permutations and combinations, the hidden patterns of Pascal's triangle, inclusion–exclusion (and why 1/e appears in Secret Santa), and the pigeonhole principle.

7 lessons~40 min0/7 complete
1

Counting Principles

Multiply choices, arrange things in order.

  1. The Multiplication PrincipleChoices multiply
  2. ArrangementsPermutations and factorials
2

Choosing

Combinations and Pascal’s triangle.

  1. CombinationsWhen order doesn’t matter
  2. Pascal’s TriangleA triangle full of patterns
  3. Stars & BarsSharing things out
3

Clever Counting

Overlaps and guarantees.

  1. Inclusion–ExclusionCorrecting for overlaps
  2. The Pigeonhole PrincipleGuarantees from counting