kombinación

Kombinación, often written combinación in Spanish, is a term used across languages to denote the act or result of combining elements. In mathematics, the standard Spanish form is combinación, but the concept is widely recognized under similar spellings in other languages.

In mathematics, a combinación refers to a selection of r elements from a set of n, where the order of selection does not matter and repetitions are typically not allowed. The number of such combinations is given by the binomial coefficient C(n, r) = n! / (r!(n−r)!). This concept is a fundamental part of combinatorics and contrasts with permutations, where order does matter.

Common applications include counting and counting-based probability. For example, choosing 3 students from a class of 20, or selecting 2 cards from a standard deck, uses combinations to determine the number of possible selections. Combinatorial methods underpin many probability calculations, statistical designs, and algorithmic analyses.

Beyond mathematics, combinación can denote a general fusion or mixture of elements, ideas, or components. In everyday language, it often means a sensible or advantageous pairing of items. In some contexts, the term is used in compounds such as “combinación de números” or as a synonym for a code or lock combination.

See also: combinatorics, binomial coefficient, permutation, combination lock.