api: "YAML JSON TOON Database"
version: 1.0.0
format: json
dataset:
  slug: combinatorics-fundamentals
  title: "Combinatorics Fundamentals"
  description: "Core counting principles and combinatorial formulas."
  category: Mathematics
  category_slug: mathematics
  tags: "math,combinatorics,counting,permutations,combinations"
  view_count: 0
data
  [7]{principle,description,formula}:
    "Product Rule","If task A has m ways and task B has n ways, both can be done in m * n ways.","m * n"
    "Sum Rule","If tasks are mutually exclusive with m and n ways, total is m + n.","m + n"
    Permutations,"Ordered arrangements of r elements from n items.","P(n,r) = n! / (n - r)!"
    Combinations,"Unordered selections of r elements from n items.","C(n,r) = n! / (r!(n-r)!)"
    "Permutations with Repetition","Arrangements when some elements are identical.","n! / (n1! * n2! * ... * nk!)"
    "Pigeonhole Principle","If n items are placed into m containers and n > m, some container has >= 2 items.",ceil(n/m)
    "Binomial Theorem","Expansion of (a + b)^n.","(a+b)^n = Sum C(n,k) * a^(n-k) * b^k"