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Combinatorics Formulas
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Combinatorics
Catalan Number
C_n=\frac{1}{n+1}\binom{2n}{n}Counts many recursively structured objects such as balanced parentheses and polygon triangulations.
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Inclusion–Exclusion for Two Sets
|A\cup B|=|A|+|B|-|A\cap B|Counts elements in a union without counting the intersection twice.
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Pigeonhole Principle Bound
\max_i n_i\ge\left\lceil\frac{N}{m}\right\rceilGuarantees that at least one of m containers holds at least the ceiling of N divided by m objects.
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