Pronunciation: /ˌkɒm.bəˈneɪ.ʃən/ Explain
A combination is all possible combinations of
k elements of a set of n
objects without considering order. 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 !
Factorial is defined as n! = 1 · 2 ·
3 · … · n
A simple example is
One can verify this using a set of two objects, for example
How many ways can one
of these two objects be selected? There are two ways:
Another example is
To verify this, start with a set of five objects:
How many ways can these be listed without regard to order?
- McAdams, David E.. All Math Words Dictionary, combination. 2nd Classroom edition 20150108-4799968. pg 36. Life is a Story Problem LLC. January 8, 2015. Buy the book
- Grinstead, Charles M. and Snell, J. Laurie. Introduction to Probability. pp 92-119. Last Accessed 6/25/2018. http://www.dartmouth.edu/~chance/teaching_aids/books_articles/probability_book/amsbook.mac.pdf. Buy the book
- Smith, Charles. A treatise on algebra. pp 282-288. www.archive.org. Macmillan and Company. 1892. Last Accessed 6/25/2018. http://www.archive.org/stream/cu31924060184433#page/n307/mode/2up/search/combination. Buy the book
- 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. 4/13/2019. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/c/combination.html.
12/21/2018: Reviewed and corrected IPA pronunication. (McAdams, David E.)
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.)