1. 12-6 Counting Principle and Permutations
Goals:
Use the fundamental counting principle to count the number of ways an event can happen.
Use permutations to count the number of ways an event can happen.

2. Think about going to a Deli
4 meats: ham, turkey, bologna, roast beef
3 cheeses: American, provolone, Swiss
3 breads: white, wheat, rye
How many different sandwiches could be made?
To answer the question, we could:
List all of the options…
Use a tree diagram…
Use the Fundamental Counting Principle

3. Turkey & American on white
Turkey & American on wheat
Turkey & American on rye
Turkey & provolone on white
Turkey & provolone on wheat
Turkey & provolone on rye
Turkey & Swiss on white
Turkey & Swiss on wheat
Turkey & Swiss on rye
Roast Beef & American on white
Roast Beef & American on wheat
Roast Beef & American on rye
Roast Beef & provolone on white
Roast Beef & provolone on wheat
Roast Beef & provolone on rye
Roast Beef & Swiss on white
Roast Beef & Swiss on wheat
Roast Beef & Swiss on rye
Ham & American on white
Ham & American on wheat
Ham & American on rye
Ham & provolone on white
Ham & provolone on wheat
Ham & provolone on rye
Ham & Swiss on white
Ham & Swiss on wheat
Ham & Swiss on rye
Bologna & American on white
Bologna & American on wheat
Bologna & American on rye
Bologna & provolone on white
Bologna & provolone on wheat
Bologna & provolone on rye
Bologna & Swiss on white
Bologna & Swiss on wheat
Bologna & Swiss on rye

4. Ham
American
White
Wheat
Rye
Provolone
Swiss
Turkey
American
White
Wheat
Rye
Provolone
Swiss
Bologna
American
White
Wheat
Rye
Provolone
Swiss
Beef
Roast
American
White
Wheat
Rye
Provolone
Swiss

5. Vocabulary
Fundamental Counting Principle – to find the number of ways a series of events can happen you just have to multiply the possibilities together.
Deli example:
4 meats: ham, turkey, bologna, roast beef
3 cheeses: American, provolone, Swiss
3 breads: white, wheat, rye
4 * 3 * 3 = 36

6. Examples Course Selection:
2 Math, 2 Science, 3 Social Studies, 4 English
Police Sketch Artist:
195 hairlines, 99 eyes, 89 noses, 105 mouths, 74 chins
License Plates:
3 letters and 2 digits
Password:
6 letters and 1 digit
48 choices
13,349,986,650 choices
1,757,600 choices
3,089,157,760 choices

7. Vocabulary Factorial: Examples: On Calculator: MATH  PRB  !
Used to multiply numbers when you are multiplying an integer times every integer smaller than it.
Symbol: !
Examples: 3! 7!
On Calculator: MATH  PRB  !
= 3 * 2 * 1
= 6
= 7 * 6 * 5 * 4 * 3 * 2 * 1
= 5040

8. Examples 6! How many ways can you arrange the letters of SMILE ?
How many ways can you arrange the letters of GRADES?
How many ways can you arrange the letters of EQUATIONS?
= 720
= 60,480
5! = 120
6! = 720
9! = 362,880

9. Jaime, Shana, Otis, Abigail, and Ernesto are lining up to take a picture on the beach. How many different ways can they line up next to each other?
A. 100
B. 240
C. 60
D. 120

10. Vocabulary Permutations:
The number of ways objects can be put in order.
Symbol: nPr OR P(n,r)
Formula:
n is the total number of items (bigger #)
r is the number being put in order (smaller #)
On Calculator: MATH  PRB  nPr

11. Examples How many ways could I arrange the seats in this classroom?
How many ways could we choose a President, Vice President, Treasurer and Secretary?
You are going to visit 6 out of 10 colleges. How many orders could you visit them?
12 skiers are in a competition. How many ways could there be first, second and third place winners?
151,200
1,320

12. The addresses of the houses on Bridget’s street each have four digits and no digit is used more than once. If each address is made up from the digits 0–9, how many different addresses are possible?
A. 24
B. 210
C. 5040
D. 151,200

13. Practice
Worksheet – “12-6 Fundamental Counting Principle and Permutations”

14. Homework
Page P36 #12,13,20
Pages #1,11-15,28,29