Difference between revisions of "Combination"
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== Examples == | == Examples == | ||
− | * [ | + | * [[2005_AIME_II_Problems/Problem_1 | 2005 AIME II Problem 1]] |
* [http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=45&year=2000&p=385889 AIME 2000II/5] | * [http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=45&year=2000&p=385889 AIME 2000II/5] | ||
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== See also == | == See also == |
Revision as of 18:58, 21 July 2006
Introduction
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
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