Types of Permutations

There are two types of Permutations: Permutations with Repitition and Permutations without Repitition.

Permutation with Repitition- This is the easiest to calculate.When you have * n* things to choose from ... you have

*choices each time!*

**n**So when choosing * r* of them, the permutations are:

**n × n × ... (r times) = n ^{r }**

(Because there are **n** possibilities for the first choice, THEN there are **n** possibilites for the second choice, and so on.)

Example: in the lock above, there are 10 numbers to choose from (0,1,..9) and you choose 3 of them:

**10 × 10 × ... (3 times) = 10 ^{3} = 1000 permutations**

So, the formula is simply:

n^{r} |

where is the number of things to choose from, and you choose n of themr(Repetition allowed, order matters) |

- Permutations without Repitition - In this case, you have to
**reduce**the number of available choices each time.

For example, what order could 16 pool balls be in?

After choosing, say, number "14" you can't choose it again.So, your first choice would have 16 possibilites, and your next choice would then have 15 possibilities, then 14, 13, etc. And the total permutations would be:

**16 × 15 × 14 × 13 ... = 20,922,789,888,000**

But maybe you don't want to choose them all, just 3 of them, so that would be only:

In other words, there are 3,360 different ways that 3 pool balls could be selected out of 16 balls.