Combination

Pronunciation: /ˌkɒm bəˈneɪ ʃən/ Explain

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. Grinstead, Charles M. and Snell, J. Laurie. Introduction to Probability. pp 92-119. Last Accessed 8/6/2018. http://www.dartmouth.edu/~chance/teaching_aids/books_articles/probability_book/amsbook.mac.pdf.
  2. Smith, Charles. A treatise on algebra. pp 282-288. www.archive.org. Macmillan and Company. 1892. Last Accessed 8/6/2018. http://www.archive.org/stream/cu31924060184433#page/n307/mode/2up/search/combination. Buy the book

More Information

  • McAdams, David E.. Factorial. allmathwords.org. All Math Words Encyclopedia. Life is a Story Problem LLC. 6/27/2018. http://www.allmathwords.org/en/f/factorial.html.

Cite this article as:

McAdams, David E. Combination. 6/25/2018. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/c/combination.html.

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Revision History

6/25/2018: Removed broken links, updated license, implemented new markup, updated GeoGebra apps. (McAdams, David E.)
1/14/2010: Added "References". (McAdams, David E.)
1/12/2010: Added "References". (McAdams, David E.)
11/27/2008: Changed equations to images. Added Dictionary.com to 'More Information' (McAdams, David E.)
7/7/2008: Changed equations from images to Latex. (McAdams, David E.)
4/24/2008: Initial version. (McAdams, David E.)

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