## Permutations

### Permutations: Learn

A permutation is an arrangement in which order is important. The notation for permutations is P(n,r) which is the number of permutations of "n" things if only "r" are selected.

For example, if 5 students take a test, then we could rank them by who got the best grade. That would be a case where order matters.

Let's assume that Alice (A), Brooke (B), Carol (C), Dominick (D), and
Edward (E) all took
the test, and that we want to give awards to students who received best
and second-best scores. Then the possibilities could be:

AB, AC, AD, AE, BA, BC, BD, BE,

CA, CB, CD, CE, DA, DB, DC, DE,

EA, EB, EC, ED

(20 total possibilities)

But that's a lot of writing out possibilities! We can use a formula that involves factorials instead:

P(n,r) =In our example above, we have 5 students (n) and we are concerned about ranking 2 of them (r).

P(5,2) =Notice how after writing out the factorial in the fraction, you can start to reduce the fraction by canceling most of the factors. This makes factorials the easy way to find how many possible permutations are available.

### Permutation: Practice

#### Find the number of permutations.

00:00

P(,) =

Press the Start Button To Begin

You have
0
correct and
0
incorrect.

This is
0
percent correct.

### Play

Game Name | Description | Best Score |
---|---|---|

How many correct answers can you get in 60 seconds? | 0 | |

Extra time is awarded for each correct answer.
Play longer by getting more correct. |
0 | |

How fast can you get 20 more correct answers than wrong answers? | 999 |

### Explore

#### Math Lessons by Grade

#### Math Topics

- Addition
- Algebra
- Comparing
- Counting
- Decimals
- Division
- Equations
- Estimation and Mental Math
- Exponents
- Fractions
- Geometry
- Measurement
- Money
- Multiplication
- Naming Numbers
- Patterns
- Percents and Ratios
- Place Value
- Properties
- Statistics
- Subtraction