1. Unit 2 - Permutations and Organized Counting
Handout Unit 2 Outline
Learning Goals
Warm-up activity
Note - Fundamental Counting Principle or multiplicative rule
Note - Indirect Method
Note - Additive Counting Principle or Rule of sum

2. Organized Counting Learning Goals
I can draw tree diagrams to model counting problems.
I can use the fundamental counting principle (multiplicative principle) additive counting principle (rule of sum) and indirect method to solve counting problems.

3. Methods of Counting Solution 1 Warm - Up
NDSS is holding their annual student council elections. There are 3 candidates for President, 3 for Vice-President, 5 for Social Co-Ordinator and 2 for Communications. Assuming there are no running-mates (every position is chosen independent of others) how many different councils are possible?
Solution 1

4. Methods of Counting Solution 2 Warm - Up
NDSS is holding their annual student council elections. There are 3 candidates for President, 3 for Vice-President, 5 for Social Co-Ordinator and 2 for Communications. Assuming there are no running-mates (every position is chosen independent of others) how many different councils are possible?
Solution 2

5. Methods of Counting - Tree diagrams
Combinatronics
"branch of mathematics dealing with ideas and methods for counting"
Textbook page 225
Example 1
Chez-Piggy restaurant offers a dinner special where you can choose 1 appetizer, 1 entree and 1 dessert off a special menu. Appetizers include a spinach salad, frites or soup. Entree's include fish, chicken or steak. Desserts include chocolate mousse, pavlova, and fresh fruit. What is the total number of meal possibilities for the special menu?
Solution
Given -
Required -
Solution -

6. Methods of Counting - Tree diagrams
Example 1 - Tree Diagram solution
Chez-Piggy restaurant offers a dinner special where you can choose 1 appetizer, 1 entree and 1 dessert off a special menu. Appetizers include a spinach salad, frites or soup. Entree's include fish, chicken or steak. Desserts include chocolate mousse, pavlova, and fresh fruit. What is the total number of meal possibilities for the special menu?
Solution
chocolate mousse
fresh fruit
pavlova
fish
chicken
steak
spinach
salad
frites
soup

7. Methods of Counting - MCP
Example 1 - Product Rule solution
Multiplicative Counting Principle (fundamental counting principle)
Chez-Piggy restaurant offers a dinner special where you can choose 1 appetizer, 1 entree and 1 dessert off a special menu. Appetizers include a spinach salad, frites or soup. Entree's include fish, chicken or steak. Desserts include chocolate mousse, pavlova, and fresh fruit. What is the total number of meal possibilities for the special menu?
Solution
Given -
Required -
Solution - Total # =

8. Methods of Counting - MCP
Multiplicative Counting Principle (fundamental counting principle)
The multiplicative counting principle is used when a problem has several stages with separate choices. The total number of choices is
m x n x p...
m = total number of first stage choices
n = total number of second stage choices
p = total number of third stage choices
and so on

9. Methods of Counting - Rule of Sum
Example 2
How many ways are there of selecting either a red face card or a black ace from a standard deck of cards?
Solution
Given -
Required -
Solution -

10. ways in which one of these actions can occur
Methods of Counting - Rule of Sum
Additive Counting Principle or Rule of Sum
If one mutually exclusive action can occur in m ways, and a second in n ways a third in p ways and so on, then there are
m + p + n
ways in which one of these actions can occur

11. Methods of Counting - Indirect Method
Example 3
How many 5 digit locker numbers can be created if at least one of the numbers is repeated?
Given - Lockers with 5 numbers =
Lockers with non-repeats
Required - Lockers with at least 1 repeat
Solution -