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A permutation is an arrangement of all or part of a
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.
number of permutations of n
objects taken r
at a time is
nPr = n(n - 1)(n
- 2) ... (n - r + 1) = n! / (n - r)!
Note the distinction between a permutation and a
. 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.