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The product of all positive integers less than or equal to a given positive integer.

An arrangement of objects in a specific order.

A selection of objects where order does not matter.

The number of ways to choose a subset of k elements from a set of n elements without regard to the order of selection.

A formula for expressing the powers of sums, which generalizes the binomial coefficients.

The number of ways to divide n items into multiple groups of various sizes.

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.

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.

The set of all ordered pairs (a, b) where a is in set A and b is in set B.

The number of unique arrangements of a multiset where repetitions of elements are allowed.

A collection of distinct objects, considered as an object in its own right.

A set of which all elements are also contained in another set.

The set of all subsets of a set, including the empty set and the set itself.

Two or more sets that have no element in common.

The set containing all elements from all sets being considered.

The set containing all elements that are common to all sets being considered.

The set of elements that are in one set but not in another.

The set of elements that are in either of two sets but not in their intersection.

The number of elements in a set.