# 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

1. 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
2. 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
3. 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. https://www.allmathwords.org/en/f/factorial.html.

McAdams, David E. Combination. 4/13/2019. All Math Words Encyclopedia. Life is a Story Problem LLC. https://www.allmathwords.org/en/c/combination.html.

### Revision History

12/21/2018: Reviewed and corrected IPA pronunication. (McAdams, David E.)