kombinatsioonideks

Kombinatsioonideks is an Estonian form that can be understood as the translative of “kombinatsioon” or, in a mathematical context, as referring to combinations. In mathematics, the term combinaatsioon (plural kombinatsioonid) denotes a selection of elements from a set where the order of selection does not matter. The field dealing with such counting problems is combinatorics.

A fundamental concept is a combination of n distinct items taken k at a time. The number of such combinations is written as n choose k and calculated as n!/(k!(n−k)!). For example, from a set of four elements {A, B, C, D}, the number of 2-element combinations is 6: AB, AC, AD, BC, BD, CD. The key feature is that AB and BA are considered the same combination.

Combinations can also be taken with repetition, allowing elements to appear more than once. The count for choosing k items from n types with repetition is C(n+k−1, k). For instance, selecting 3 candies from 4 flavors with repetition yields C(6,3) = 20 combinations.

Relation to other concepts is important: a permutation counts ordered arrangements, while a combination ignores order. The concept connects to areas such as probability, statistics, card games, lotteries, and experimental design. It also relates to Pascal’s triangle and the binomial theorem, where binomial coefficients enumerate the coefficients in expansions.

In Estonian grammar, the suffix -deks denotes a translative or transformative meaning, indicating a state or designation into which something is placed, including phrases referring to combinations.