kombinacija

Kombinacija is a term used in many Slavic languages to denote a combination, a selection, or a configuration of elements. In mathematics and everyday language, it often refers to choosing items from a set where the order of selection may or may not matter, depending on the context.

In combinatorics, a combination refers specifically to a selection of k elements from a set of n elements where the order does not matter. The number of such combinations is denoted C(n, k) and calculated as C(n, k) = n! / (k! (n − k)!). If repetition is allowed, the count is given by C(n + k − 1, k) (multiset combinations). By contrast, when order matters, the related concept is a permutation, with nPk = n! / (n − k)!.

Examples help illustrate the idea: choosing 3 items from a set of 5, such as {A, B, C, D, E}, yields C(5, 3) = 10 possible combinations. If the order of selection were important, the count would be 5P3 = 60, which is a permutation, not a combination. If repetition is allowed, such as selecting 3 letters from 5 types with repetition, the number of combinations is C(7, 3) = 35.

Beyond math, combinación is used in everyday language to describe color schemes, feature assortments, or any set of elements considered together. Related concepts include permutation, combination with repetition, and the binomial coefficient. The term derives from Latin combinare, meaning to place together.