Combination

A selection of objects in which order does not distinguish outcomes. In counting, a combination is a subset of a specified size chosen from a larger set.

Binomial coefficient: The number of ways to choose a fixed-size subset from a finite set. It counts combinations of a given size from a set of distinct objects.
Set: A collection of distinct objects considered without regard to order. A combination is a subset, so set membership captures its order-free nature.
Lottery: A game of chance in which prizes depend on randomly selected outcomes. A ticket's selected numbers form a combination when their draw order does not matter.
Permutation: An ordered arrangement of distinct objects selected from a set. It is the order-sensitive counterpart to an ordinary combination.
Factorial: The product of all positive integers up to a given integer, with zero factorial equal to one. Factorials express the number of arrangements and yield the combination formula.
Subset: A set whose elements all belong to another set. A combination of distinct objects is precisely a subset of the specified size.
Binomial distribution: A probability distribution for the number of successes in a fixed number of independent trials with equal success probability. Its probability formula counts which trial positions produce the specified number of successes.
Variation (combinatorics): An ordered selection of a specified number of objects from a larger set. It counts chosen objects in sequence, unlike combinations.
Pascal's triangle: A triangular array whose entries are binomial coefficients and whose rows follow an addition rule. Each entry gives a combination count, and neighboring entries combine through Pascal's identity.
Cardinality: The number of elements in a set. The size of the chosen subset determines which combinations are being counted.

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