Combination
Pronunciation: /ˌkɒm.bəˈneɪ.ʃən/ Explain
A combination is all possible combinations of
k elements of a set of n
objects without considering order.^{[2][3]} 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
n! = 1 · 2 ·
3 · … · n.
A simple example is
One can verify this using a set of two objects, for example
{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
- 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
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. 4/13/2019. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/c/combination.html.
Image Credits
Revision History
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.)