Permutation

An arrangement of things in a definite order with no repetitions is a **permutation**. For example, RAT, RTA, ART, ATR, TRA, and TAR are all different arrangements of the three letters R, A and T. Notice that order is important and there are no repetitions. Finding the number of ways to arrange 3 letters without making a list can be done using the **Fundamental Counting Principle**.

This is the Powerpoint slides that I've used in class. You can download it and review the main points covered.

If event //M// can occur in //m// ways and, after it has occurred event //N// can occur in //n// ways, then event //M// followed by event //N// can occur in //m// x //n// ways**.**
 * Fundamental Counting Principle**

Refer to the earlier example**,** there are 3 ways to choose the first letter, two ways to choose the second letter, and one way to choose the third letter. Thus there are 3 x 2 x 1 = 6 ways to arrange the letters.

In general, if there are //n// objects, then the number of possible ways to arrange the objects in a row is the product of all the natural numbers from //n// to 1, inclusive. This expression is called //**n**// **factorial** and is denoted **n!**

//n//! = //n// x (//n// - 1) x (//n// - 2) x. . . x 3 x 2 x 1

You can view these 3 video clips on how to solve permutation questions, starting from the basics.

Exercise 1 media type="custom" key="856407"

Exercise 2 media type="custom" key="856403"

Exercise 3 media type="custom" key="856415"

Try these exercises. [To be continued...]