# Statistics and Probability Dictionary

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### Permutation

A permutation is an arrangement of all or part of a
set
of objects, *with* regard to the order of the arrangement.

For example, suppose we have a set of three letters: A, B, and C. We might ask how many ways we can arrange 2 letters from that set. Each possible arrangement would be an example of a permutation. The complete list of possible permutations would be: AB, AC, BA, BC, CA, and CB.

When they refer to permutations, statisticians use a specific terminology. They
describe permutations as *n* distinct objects taken *r* at a time.
Translation: *n* refers to the number of objects from which the
permutation is formed; and *r* refers to the number of objects used to
form the permutation. Consider the example from the previous paragraph. The
permutation was formed from 3 letters (A, B, and C), so *n* = 3; and the
permutation consisted of 2 letters, so *r* = 2.

**Computing the number of permutations.**The number of permutations of

*n*objects taken

*r*at a time is

_{n}P

_{r}= n(n - 1)(n - 2) ... (n - r + 1) = n! / (n - r)!

Note the distinction between a permutation and a
combination
. A combination focuses on the selection of objects *without*
regard to the order in which they are selected. A permutation, in contrast,
focuses on the arrangement of objects *with* regard to the order in which
they are arranged. Thus, the letters AB and BA represent two different
permutations, because the order is different. However, they represent only 1
combination; because order is not important in a combination.

See also: | Rules of Counting | Event Counter |