Kombinaation

Kombinaation is a concept in combinatorics that refers to the selection of objects from a finite set where the order of selection does not matter. When choosing r elements from a set of n distinct elements, the number of possible combinations is given by the binomial coefficient C(n, r) = n! / (r!(n − r)!). This quantity is also read as “n choose r.”

An example is selecting a 5-card hand from a standard deck of 52 cards. The number of possible hands is C(52, 5) = 2,598,960. The key distinction from permutations is that in combinations, different orderings of the same elements are counted as a single outcome.

There are several variants. Combinations with repetition allow repeated elements in a selection, with the number of r-element multisets drawn from an n-element set given by C(n + r − 1, r). When repetition is not allowed, the basic C(n, r) formula applies. For larger selections, recursive or generating-function approaches can be used, and the numbers appear in Pascal’s triangle.

Combinations connect to broader ideas in probability and algebra. The binomial theorem expresses coefficients as combinations, and Pascal’s triangle provides a compact visualization of C(n, r). In practical terms, combinations are used in lottery, card games, experimental design, genetics, and any situation requiring counting distinct subsets.

See also: permutation, binomial coefficient, factorial, Pascal’s triangle, combinations with repetition.