1. Apply the Counting Principle and Permutations
Section 10.1
Apply the Counting Principle and Permutations

2. California Standard:
18.0: students use fundamental counting principles to compute combinations and permutations.

3. By following instructions, students will be able to:
OBJECTIVE(S):
By following instructions, students will be able to:
Use the fundamental counting principle and permutations.

4. EXAMPLE 1: Beetle Fundamental Counting Principle: Jetta Touareg
A Volkswagen dealership offers three different types of cars (Beetle, Jetta, and Touareg). Each type comes in two different colors (Red and Black). How many choices does the dealership offers?
Beetle
Fundamental Counting Principle:
(3 types of cars)(2 different colors) = 6 different choices
Jetta
Touareg

5. FUNDAMENTAL COUNTING PRINCIPLE
Two Events
If one event can occur in m ways and another can occur in n ways, then
Two or More Events
If three events occur in m, n, and p ways, then

6. EXAMPLE 2:
You are framing a picture. The frames are available in 12 different styles. Each style is available in 55 different colors. You also want blue mat board, which is available in 11 different shades of blue How many ways can you frame the picture? 6

7. EXAMPLE 3:
The standard configuration for a Texas license plate is 1 letter followed by 2 digits followed by 3 letters.
How many different license plates are possible if letters and digits can be repeated?
How many different license plates are possible if letters and digits cannot be repeated? 7

8. U-TRY#1:
The standard configuration for a California License plate is 1 number followed by three letters followed by 3 numbers with the exclusion of I, O, and Q in the first or third alpha position of the alpha numeric series. How many different license plate are possible with this exclusion?

9. DEFINITIONS Permutation
An ORDERING of n objects is called a permutation.
Ex. ABC can be written in 6 different order.
ABC, ACB, BAC, BCA, CAB, and CBA
Factorial

10. EXAMPLE 4:
Ten teams are competing in the final round of the Olympic four-person bobsledding competition.
In how many different ways can the bobsledding teams finish the competition? (Assume there are no ties.)
In how many different ways can 3 of the bobsledding teams finish, first, second, and third to win the gold, silver, and bronze medals? 10

11. U-TRY #2:
In example 4, how would the answers change if there were 12 bobsledding teams competing in the final round of the competition?

12. KEY CONCEPT Permutations of n objects taken r at a time.
The number of permutations of r objects taken from a group of n distinct objects is denoted by

13. EXAMPLE 5:
You are burning a demo CD for your band. Your band has 12 songs stored on your computer However, you want to put only 4 songs on the demo CD. In how many orders can you burn 4 of the 12 songs onto the CD? 13

14. U-TRY #3:
Find the number of permutations. a) b) c) d)

15. KEY CONCEPT Permutations with Repetition.
The number of distinguishable permutations of n objects where one object is repeated
times and another is repeated
times, and so on, is:

16. EXAMPLE 6:
Find the number of distinguishable permutations of the letters in:
EYE
MIAMI
TALLAHASSEE 16

17. U-TRY #4:
Find the number of distinguishable permutations of the letters in the word.
a) MALL
b) KAYAK
c) HELLO
d) KITTY

18. HOMEWORK
Sec 10.1 WS