Combination

Definition

Let $X$ be a set and let $k$ be a natural number. A $k$ -combination of $X$ is a subset $S \subseteq X$ with $|S| = k$ .

The set of all $k$ -combinations of $X$ is written $\binom{X}{k}$ .

Remarks

A combination does not record an order of its elements. Two lists with the same elements in a different order give the same combination. For $X = \{a, b, c\}$ , the 2-combinations are $\{a, b\}$ , $\{a, c\}$ and $\{b, c\}$ . The number of k-element subsets of an $n$ -element set is the binomial coefficient $\binom{n}{k}$ .

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Number of k-element subsets

Tag	`0JZSRWRBZE`
URI	`m2://0JZSRWRBZE`
Kind	definition
Writing	W1 stated
MSC	05A05
Defines	Combination

Combination

Definition

Remarks

Where this leads

Further reading

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