# Difference between revisions of "Combination"

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The common forms of denoting the number of combinations of <math>{r}</math> objects from a set of <math>{n}</math> objects is: | The common forms of denoting the number of combinations of <math>{r}</math> objects from a set of <math>{n}</math> objects is: | ||

− | * <math>{n} | + | * <math>\binom{n}{r}</math> |

* <math>{C}(n,r)</math> | * <math>{C}(n,r)</math> | ||

* <math>\,_{n} C_{r}</math> | * <math>\,_{n} C_{r}</math> |

## Revision as of 19:28, 25 September 2007

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

## Contents

## Notation

The common forms of denoting the number of combinations of objects from a set of objects is:

## Formula

## Derivation

Consider the set of letters A, B, and C. There are 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 objects from elements , there are more ways to permute them than to choose them. We have , or .

## Examples