{
    "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": [
        {
            "principle": "Product Rule",
            "description": "If task A has m ways and task B has n ways, both can be done in m * n ways.",
            "formula": "m * n"
        },
        {
            "principle": "Sum Rule",
            "description": "If tasks are mutually exclusive with m and n ways, total is m + n.",
            "formula": "m + n"
        },
        {
            "principle": "Permutations",
            "description": "Ordered arrangements of r elements from n items.",
            "formula": "P(n,r) = n! / (n - r)!"
        },
        {
            "principle": "Combinations",
            "description": "Unordered selections of r elements from n items.",
            "formula": "C(n,r) = n! / (r!(n-r)!)"
        },
        {
            "principle": "Permutations with Repetition",
            "description": "Arrangements when some elements are identical.",
            "formula": "n! / (n1! * n2! * ... * nk!)"
        },
        {
            "principle": "Pigeonhole Principle",
            "description": "If n items are placed into m containers and n > m, some container has >= 2 items.",
            "formula": "ceil(n/m)"
        },
        {
            "principle": "Binomial Theorem",
            "description": "Expansion of (a + b)^n.",
            "formula": "(a+b)^n = Sum C(n,k) * a^(n-k) * b^k"
        }
    ]
}