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Basic Combinatorics Terminology
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Factorial
The product of all positive integers less than or equal to a given positive integer.
Intersection of Sets
The set containing all elements that are common to all sets being considered.
Permutation
An arrangement of objects in a specific order.
Union of Sets
The set containing all elements from all sets being considered.
Set
A collection of distinct objects, considered as an object in its own right.
Combination
A selection of objects where order does not matter.
Difference of Sets
The set of elements that are in one set but not in another.
Symmetric Difference of Sets
The set of elements that are in either of two sets but not in their intersection.
Binomial Theorem
A formula for expressing the powers of sums, which generalizes the binomial coefficients.
Disjoint Sets
Two or more sets that have no element in common.
Inclusion-Exclusion Principle
A principle used to compute the cardinality of the union of multiple sets by including the cardinalities of the sets and excluding the cardinalities of their pairwise, triple-wise, etc., intersections.
Cartesian Product
The set of all ordered pairs (a, b) where a is in set A and b is in set B.
Power Set
The set of all subsets of a set, including the empty set and the set itself.
Binomial Coefficient
The number of ways to choose a subset of k elements from a set of n elements without regard to the order of selection.
Subset
A set of which all elements are also contained in another set.
Multinomial Coefficient
The number of ways to divide n items into multiple groups of various sizes.
Pigeonhole Principle
A principle that states if n items are put into m containers, with n > m, then at least one container must contain more than one item.
Ordered Pair
A pair of elements with order being significant, typically denoted as (a, b).
Permutation of Multisets
The number of unique arrangements of a multiset where repetitions of elements are allowed.
Cardinality of a Set
The number of elements in a set.
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