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

Combination of n objects taken k at a time.

This is read saying, "n objects taken k at a time".

The formula for calculating combinations is

Combination of n objects taken k at a time.

The symbol ! means factorial. Factorial is defined as n! = 1*2*3*..*n..

A simple example is

Two objects taken one at a time.

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

Five objects taken three at a time.

To verify this, start with a set of five objects: {a,b,c,d,e}. How many ways can these be listed without regard to order?
{a,b,c},{a,b,d},{a,b,e},{a,c,d},{a,c,e},{a,d,e},{b,c,d},{b,c,e},{b,d,e},{c,d,e}

References

  1. 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=.
  2. 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.
  3. 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.)

All Math Words Encyclopedia is a service of Life is a Story Problem LLC.
Copyright © 2005-2011 Life is a Story Problem LLC. All rights reserved.
Creative Commons License This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License