Combination
Pronunciation: /ˌkɒm bəˈneɪ ʃən/ ?
A combination is all possible combinations of
k elements of a set of n
objects without considering order.^{[1]} If one is not considering order, the combination
ABC is the same as the combination
ACB. The mathematical notation for combination is
This is read saying, "n objects taken k at a time".
The formula for calculating combinations is
The symbol
! means
factorial.
Factorial is defined as
.
A simple example is
One can verify this using a set of two objects, say
{a, b}.
How many ways can
one of these two objects be selected? There are two ways:
{a} and
{b}.
Another example is
To verify this, start with a set of five objects:
.
How many ways can these be listed without regard to order?
References
- combination. http://wordnet.princeton.edu/. WordNet. Princeton University. (Accessed: 2011-01-08). http://wordnetweb.princeton.edu/perl/webwn?s=combination&sub=Search+WordNet&o2=&o0=1&o7=&o5=&o1=1&o6=&o4=&o3=&h=.
- Grinstead, Charles M. and Snell, J. Laurie. Introduction to Probability, pp 92-119. (Accessed: 2010-01-12). http://www.dartmouth.edu/~chance/teaching_aids/books_articles/probability_book/amsbook.mac.pdf.
- Smith, Charles. A treatise on algebra, pp 282-288. Macmillan and Company, 1892. (Accessed: 2010-01-14). http://www.archive.org/stream/cu31924060184433#page/n307/mode/2up/search/combination.
More Information
- McAdams, David. Factorial. allmathwords.org. All Math Words Encyclopedia. Life is a Story Problem LLC. 2009-03-12. http://www.allmathwords.org/article.aspx?lang=en&id=Factorial.
Cite this article as:
Combination. 2010-01-14. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/c/combination.html.
Translations
Image Credits
Revision History
2010-01-14: Added "References" (
McAdams, David.)
2010-01-12: Added "References" (
McAdams, David.)
2008-11-27: Changed equations to images. Added Dictionary.com to 'More Information' (
McAdams, David.)
2008-07-07: Changed equations from images to Latex (
McAdams, David.)
2008-04-24: Initial version (
McAdams, David.)