9-4: Permutations

This is Chapter 9 Section 4: Permutations (or as the book refers to it: "Probabilities of Various Permutations" -- which is a mouthful.

Definition: Permutation
A Permutation is a way to count the number of outcomes when order is
important.

The best way to explain this is through examples. Here are some examples of different times a permutation may help you:

Example 1
We want to form a line with three students to take a picture. How many ways can we do this, assuming there are twelve of us in the classroom:

12 11 10

There would be 1,320 different ways to take this picture. (12x11x10)

Example 2
What if there is a restriction? For example, I am short and want to be in the middle. Let's see how we can do this if we want to be able to take 5 photos:

11 10 1 9 8

The 1 is me in the middle because there is only one way to make this work and the rest is 11, 10, 9 and 8.

Factorials!
This is what makes our life easier. Let's say that we had twelve students and twelve different ways to take the photo... so it's...

12 11 10 9 8 7 6 5 4 3 2 1

The easiest way to write this is: 12!

Our calculator can help make this really easy:

1. Enter the number
2. Go to Math and then PRB (probability)
3. Scroll to the ! which stands is the option for a factorial.

By the way, the answer is 479, 001, 600

Here's a hint, fill the restrictions first and then continue with the factorial.

Example Problem

You are designing a new frozen yogurt shop and must decide the order for all the different toppings. You know that there are 21 choices and that "Strawberry" must be the first choice. Determine the possible amount of ways to organize your toppings.

Answer...

1 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1

This is the breakdown of my choices. Note that there is only one option for the first topping (Strawberry). To solve, use 1 x 20! in your calculator which gives you...

2.43 x 10 ^ 18

Which is a lot of different ways to organize your store.

Extra Help:

http://mathforum.org/dr.math/faq/faq.comb.perm.html

Describes permutations as well as combinations-- so only look at the first part. It's a fairly good explanation.

Amira you're up next!

Soo... I would like to share with everyone my new favoritest thing ever. In fact, over the weekend I went and brought two large ones home which I'm eating right now.

I suggest that you read about this amazing non-fat all natural creation and then visit your nearest Pinkberry! (Mine's Studio City, but they will open in Old Town sometime this year) Don't get fooled and visit Roseberry in Glendale-- it's not the same. Ironically enough, Pinkberry is in many ways a copy of a huge Korean chain called Iceberry... but enough talking.