kombinasi

Kombinasi, or combinations, is a fundamental concept in combinatorics describing the selection of items from a finite set where the order of selection does not matter. If a set has n distinct elements and one chooses r of them, the number of possible selections is called a combination and is denoted C(n, r) or “n choose r.” The value is calculated as n! / (r!(n − r)!). In this sense, order is irrelevant: choosing A, B, and C is the same as choosing C, B, and A.

An example: from a group of 7 people, the number of ways to pick 3 is C(7, 3) = 35.

Combinations can also consider repetitions, depending on the context. Without repetition, the expression above applies. With repetition allowed (multisets), the number of r-combinations from n types is C(n + r − 1, r). This is related to stars and bars techniques.

The concept connects to the binomial coefficient and the binomial theorem: C(n, k) appears as coefficients in the expansion of (x + y)^n and can be found in Pascal’s triangle.

Applications of kombinasi include probability calculations, statistical sampling, card games, lotteries, and resource allocation problems, where the order of selection is irrelevant.

See also: permutation, binomial coefficient, stars and bars, Pascal’s triangle, combinatorial identities.