information:classification
n -tuples of m -sets

In discrete mathematics, especially combinatorics and finite probability theory, n -tuples arise in the context of various counting problems and are treated more informally as ordered lists of length n. n -tuples whose entries come from a set of m elements are also called arrangements with repetition, permutations of a multiset and, in some non-English literature, variations with repetition. The number of n -tuples of an m -set is m. This follows from the combinatorial rule of product. If S is a finite set of cardinality m, this number is the cardinality of the n -fold Cartesian power S × S × ⋯ × S. Tuples are elements of this product set.