A permutation is a mathematical technique that determines the number of possible arrangements in a set when the order of the arrangements matters. In other words, the arrangements ab and be in permutations are considered different arrangements, while in combinations, these arrangements are equal.

Permutations and combinations, the various ways in which objects from a set may be selected, generally without replacement, to form subsets. This selection of subsets is called a permutation when the order of selection is a factor, a combination when order is not a factor.

The difference between combinations and permutations is ordering. With permutations we care about the order of the elements, whereas with combinations we don’t. For example, say your locker “combo” is 5432. If you enter 4325 into your locker it won’t open because it is a different ordering (aka permutation).

Permutation can be classified in three different categories:

• Permutation of n different objects (when repetition is not allowed)
• Repetition, where repetition is allowed.
• Permutation when the objects are not distinct (Permutation of multi sets)

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. The permutation was formed from 3 letters (A, B, and C), so n = 3; and the permutation consisted of 2 letters, so r = 2.

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.

3*3*3=27 unique possibilities. This number is small enough to enumerate the possibilities to help your understanding (like the other tutors did), but the digits^base expression (with “^” meaning exponentiation) is important.