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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.
The binomial theorem expands (x + y)^n into a sum of terms using binomial coefficients that count how many ways to choose k items from n.
Stars and Bars counts the ways to distribute n identical items into k distinct bins using combinations.
Permutations count ordered selections, while combinations count unordered selections.