1. Counting Principles
NOTES
Coach Bridges

2. The Fundamental Counting Principle
If one event can occur in “m” ways and a second event can occur in “n” ways, the number of ways the two events can occur in sequence is m x n
This rule can be extended for any number of events occurring in sequence.

3. Example of Counting Principle
You are purchasing a new car. Using the following manufacturers, car sizes, and colors, how many different ways can you select one manufacturer, one car size and one color?
Manufacturer: Ford, GM, Chrysler
Car Size: Small, Medium
Color: White (W), Red (R), Black (B), Green (G)

4. Answer
3 x 2 x 4 = 24
So there are 24 ways to select one manufacturer, one car size, and one color
Now draw a Tree diagram using the information!

5. Permutations
Is an important application of the Fundamental Counting Principle and determines the number of ways that “n” objects can be arranged in order
An ordered arrangement of objects
The number of different permutations of “n” distinct objects is n!.

6. Expression n! The expression “n!” is read as n factorial
n! = n x (n – 1) x (n – 2) x (n – 3)……..
Ex.
0! = 1
1! = 1
2! = 2 x 1 = 2
3! = 3 x 2 x 1 = 6

7. Example
The women’s hockey teams for the 2010 Olympics are Canada, Sweden, Switzerland, Slovakia, United States, Finland, Russia, and China. How many different final standings are possible?

8. Other Permutations Permutation of “n” objects taken “r” at a time
Used when you want to choose some of the objects in a group and put them in order
Distinguishable Permutations
The number of ways “n” objects can occur, where you have many different types

9. “Order Matters” & Combinations
Permutations are used when order matters
Combination is used when order does not matter
The number of ways to choose “r” objects from “n” objects without regard to order
Refer to Table on Pg. 171