kombinacja

Kombinacja is a Polish term with several related meanings. In everyday Polish, it denotes an arrangement, plan, or scheme to achieve a goal. It can have neutral uses, as in a planned sequence of moves, or more negative connotations as a shortcut or backroom deal. In mathematics, kombinacja is the standard term for a combination, a selection of k elements from a set of n elements in which the order of selection does not matter and, in the basic form, repetition is not allowed.

In combinatorics, the number of k-element combinations from an n-element set is the binomial coefficient written C(n, k) or sometimes as “n choose k,” equal to n!/(k!(n-k)!). For example, from {A, B, C, D}, the number of 2-element combinations is 6: AB, AC, AD, BC, BD, CD. Variations include combinations with repetition, counted by C(n+k-1, k). Distinctions are often drawn with permutations, where order matters, counted by P(n, k) = n!/(n-k)!.

Etymology: the noun derives from the verb kombinować, meaning to combine; its use in mathematics arose to name the concept of selecting items. In culture and politics, “kombinacja” can refer to a planned arrangement or scheme, sometimes noted with skepticism, such as a coalition or backroom deal.

See also: combinatorics, binomial coefficient, permutation.