Permutation – a method of finding the combinations available for an ordered arrangment elements of a set of objects where repetition is not allowed. When we say that order is important, this means that the same element in different order is considered to be distinct.
r-permutations – elements of a given set

A Representation of Permuation:
Given a set of object {a,b,c,d,e}
The permutation of the objects include:
One-permutation = P(5,1) There are five objects from which we want to take the one permutation of. There are five possible choices: {a}, {b}, {c}, {d}, {e}

Two-permutation = P(5,2) There are 20 possible choices for two-permutation: {a,b}, {b,a}, {a,c}, {c,a}, {a,d}, {d,a}, {a,e}, {e,a}, {b,c}, {c,b}, {b,d}, {d,b}, {b,e}, {e,b}, {c,d},{d,c}, {c,e}, {c,e}, {d,e}, {e,d}
> Unlike Combinations, order is important, therefore we take into consideration the situation in which a and b are switched for example.

> The same things can be done for three, four, and five-perumations where three-permutation has 60 possible choices, four and five-permuation has 120 possible choices.

Example:

You are asked by your manager to stock the items onto the shelves. There are total of five shelves. You want to find the number of ways in which you can place five types of ink cartridges (Epson, Hewlett Packard, LexMark, Cannon and Xerox) onto the shelves.

First of all, in this problem, order is important therefore you must use permutation. Order is important because arranging an Epson in front of a Cannon, for example, is different than placing the Cannon infront of the Epson cartridge.

Since there are five places for five cartridges, we can plug this into the euqation:

P(5,5) = 5! = 120

If we were just fiven two different cartridges, then we can do the same:

P(5,2) = 20 => so there are twenty different ways to arrange two cartridges onto five different shelves.

Practice Problem:

Your mom works as a seamstress. She was asked to put up four sets of curtain, each set contain and outside curtain
and an inside curtain. Each set has a distinct color of white, light pink, light blue, and light yellow. These curtains are hung onto four main windows of the house. The owner of the house told here that she mis-match the inner curtains and the outer curtains if she liked (meaning she can arrange the outside curtain with a different colored inside curtain). You are interested in how many possible combinations in which she group these curtain with different colored outside/inside curtains (they cannot be the same) onto the four windows.