Permutations
probability
Counts ordered selections of r items from n distinct items.
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Combinations
probability
Counts unordered selections of r items from n distinct items.
Factorial
discrete math
Multiplies positive integers from 1 through n.
Binomial Coefficient
discrete math
Counts k-element subsets of an n-element set.
Inclusion-Exclusion for Two Sets
discrete math
Counts elements in a union while correcting for overlap.
Set Union Cardinality
discrete math
Expresses cardinality of a union of two finite sets.
De Morgan's Law for a Union
discrete math
The complement of a union equals the intersection of complements.
De Morgan's Law for an Intersection
discrete math
The complement of an intersection equals the union of complements.
Cartesian Product Cardinality
discrete math
Counts ordered pairs in the Cartesian product of finite sets.
Power Set Cardinality
discrete math
Counts all subsets of a finite set.
Handshake Lemma
discrete math
Relates vertex degrees to edge count in an undirected graph.
Complete Graph Edge Count
discrete math
Counts edges in a complete graph on n vertices.
Tree Edge Count
discrete math
Counts edges in a finite tree.
Graph Degree Bound
discrete math
Bounds degree of a vertex in a simple graph.
Pigeonhole Principle
discrete math
States that more objects than boxes force a repeated box.
Arithmetic Recurrence
discrete math
Defines an arithmetic sequence recursively.
Geometric Recurrence
discrete math
Defines a geometric sequence recursively.
Boolean De Morgan's Law
discrete math
Negates a conjunction using an equivalent disjunction.
Boolean De Morgan's Law for Or
discrete math
Negates a disjunction using an equivalent conjunction.