Difference between revisions of "Combination"
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* [http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=45&year=2005&p=368223 AIME 2005II/1] | * [http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=45&year=2005&p=368223 AIME 2005II/1] | ||
+ | * [http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=45&year=2000&p=385889 AIME 2000II/5] | ||
=== See also === | === See also === |
Revision as of 10:42, 19 June 2006
Contents
[hide]Definition
The number of combinations of objects from a set of objects is the number of ways the objects can be arranged with regard to order.
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 .