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combination and permutation

Contributor(s): Laura Fitzgibbons

In mathematics, combination and permutation are two different ways of grouping elements of a set into subsets. In a combination, the elements of the subset can be listed in any order. In a permutation, the elements of the subset are listed in a specific order. 

All data sets have a finite number of combinations as well as a finite number of permutations. This makes them useful for calculating probability for complex events. The more elements contained in a set, the greater the number of possible permutations and the smaller the probability that a specific permutation will occur. 

The common notations used for combination and permutation are as follows:

The number of combinations of n units consider r at a time is:

C(n,r)=          n!    

                 (n−r)!r!

The number of permutations of n units considered r at a time is:

P(n,r)=            n!    

                    (n−r)!

This was last updated in May 2018

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