1. Calculating Probability, Combinations and Permutations

2. Fundamental Counting Principle
A.K.A. Product Rule:
Multiply events together to get the total number of outcomes.
Ex A: 1 Coin: 2 outcomes
2 Coins: 2 x 2 =4 outcomes
3 Coins: 2 x 2 x 2 =8
Used to figure out the number of outcomes in a probability problem.
Your Turn: The Sandwich shop offers a $5 combo. Choose 1 from each category: There are 3 sandwich choices, 2 sides, and 3 beverages.
3 x 2 x 3 = 18

3. Permutations Are “PICKY”. Order Matters.
It is the number ways to organize outcomes when ORDER MATTERS
Think about an organized List
*remember the coin flip problem?
You found 8 permutations for the sample space!
Examples:
A Combination Lock really should be called a PERMUTATION LOCK
i.e. Your combo is , so does not work!

4. How many options? Calculating Permutations
Suppose we have 5 people in a race. How many ways can Gold, Silver and Bronze be awarded?
Options?
Make an organized list
A,B,C,D,E __, __, __
But Wait, these are just from the first 3 letters! What happens next?
ABC ACB
BAC BCA
CAB CBA

5. How many options? Calculating Permutations
Suppose we have 5 people in a race. How many ways can Gold, Silver and Bronze be awarded?
Options?
Make an organized list
A,B,C,D,E __, __, __
How about BCD, BDC,
CBD, CDB,
DBC, DCB
Hmm. Let’s try that counting principle…
5 x 4 x 3 = 60
So, we have:
ABC ACB
BAC BCA
CAB CBA

6. Is there a Formula for this stuff?
N! Factorial. The product of an integer and all integers below it

7. Combinations Are “Easy going” Order Does not Matter
But, how many ways can I PERMUTE those 3 ingredients?
Are “Easy going”
Order Does not Matter
It is the number of outcomes when order doesn’t matter
3 x 2 x 1 = 3! (Three Factorial), or 6 ways.
BUT it’s really ONE smoothie…
So, let’s get back to that... :
Example
A strawberry, apple, banana smoothie tastes the same as a banana, strawberry, apple one!
3 Choose 3 = 1

8. Try it!
So, how many ways can I PERMUTE those 3 ingredients?
Make an organized list or tree diagram
SAB, SBA
ABS, ASB
BAS, BSA
Use the Formula 3!
(3 - 3)!
= 6
9/14

9. Calculating Combinations
Consider the First problem. What if we DIDN’T care about the order?
Then these results would be the SAME!
ABC ACB
BAC BCA
CAB CBA
The question is NOW: How can I choose ANY 3 people out of the 5?
Now how many ways can 3 people can arranged without order?
Can we list them?

10. Calculating Combinations
Consider the First problem. What if we DIDN’T care about the order?
Then these results would be the SAME!
ABC ACB
BAC BCA
CAB CBA
The question is NOW: How can I choose 3 people out of the 5?
Now how many ways can 3 people can arranged without order?
Can we list them?

11. Combination Formula

12. 9/15 Do Now: In Notebooks
Use a tree diagram to determine how many ways you can choose an outfit based on 1 pair of Black shoes, Blue pants vs. black pants, and a blue or white shirt.
Is this a Permutation or Combination or Neither?
3. If possible, Write the formula to solve this problem, then use a calculator to check!

14. CLASSWORK Text pg. 969 #16-19 Use the following protocols:
Work independently first 2-3 min
Silently, using your resources
Next you may consult with an elbow partner (in YOUR ROW)
Talk on task
Talk only with partner(s)
Keep voices at level 1
Minutes 7-10 finish the assignment independently