Concepts5
∑MathIntermediate
Derangements
A derangement is a permutation with no element left in its original position, often written as !n or D(n).
#derangement#subfactorial#inclusion-exclusion+11
∑MathIntermediate
Inclusion-Exclusion Principle
The Inclusion-Exclusion Principle (IEP) corrects overcounting by alternately adding and subtracting sizes of intersections of sets.
#inclusion-exclusion#derangements#surjections+12
∑MathIntermediate
Binomial Theorem and Identities
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.
#binomial theorem#binomial coefficient#pascal's triangle+12
∑MathIntermediate
Stars and Bars
Stars and Bars counts the ways to distribute n identical items into k distinct bins using combinations.
#stars and bars#combinatorics#binomial coefficient+12
∑MathIntermediate
Permutations and Combinations
Permutations count ordered selections, while combinations count unordered selections.
#permutations#combinations#binomial coefficient+12