Difference between revisions of "Combination"

Revision as of 23:08, 23 July 2006

A combination is a way of choosing $r$ objects from a set of $n$ where the order in which the objects are chosen is irrelevant. We are generally concerned with finding the number of combinations of size $r$ from an original set of size $n$

Notation

The common forms of denoting the number of combinations of ${r}$ objects from a set of ${n}$ objects is:

${n}\choose {r}$
${C}(n,r)$
$\,_{n} C_{r}$
$C_n^{r}$

Formula

${{n}\choose {r}} = \frac {n!} {r!(n-r)!}$

Derivation

Consider the set of letters A, B, and C. There are $3!$ different permutations of those letters. Since order doesn't matter with combinations, there is only one combination of those three. In general, since for every permutation of ${r}$ objects from ${n}$ elements $P(n,r)$ , there are ${r}!$ more ways to permute them than to choose them. We have ${r}!{C}({n},{r})=P(n,r)$ , or ${{n}\choose {r}} = \frac {n!} {r!(n-r)!}$ .

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Difference between revisions of "Combination"

Revision as of 23:08, 23 July 2006

Contents

Notation

Formula

Derivation

Examples

See also

Revision as of 17:59, 21 July 2006 (view source) MCrawford (talk \| contribs) m (removed heading of first section) ← Older edit	Revision as of 23:08, 23 July 2006 (view source) Joml88 (talk \| contribs) m (Combinations moved to Combination) Newer edit →
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