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Kolmogorov’s axioms define probability as a measure on events: non-negativity, normalization, and countable additivity.
A derangement is a permutation with no element left in its original position, often written as !n or D(n).
The Inclusion-Exclusion Principle (IEP) corrects overcounting by alternately adding and subtracting sizes of intersections of sets.
Stars and Bars counts the ways to distribute n identical items into k distinct bins using combinations.