1. Fundamental Counting

2. How do you count? Try counting these dots… 5 7 5×7= 35 So, there are 35 dots. Is this any easier?

3. Problem 1 – What is for lunch? How many different lunches can be made if a student must select one item from each category. beveragemain coursedessert Spritehot dogapple milkgrilled cheese sandwichmuffin coffeebagel & cream cheese egg salad sandwich

4. Problem 2 – PIN Numbers Using only the digits 0 – 9, how many different 4 digit PIN numbers can be made?

5. Problem 3 – License Plates Each license plate uses 4 letters followed by 3 numbers. How many different license plates can be made in this pattern?

6. The Fundamental Principle of Counting If you have a number of decisions to make, each of which is not influenced by the results of the other decisions, the total number of ways is the product of the number of possibilities for each decision.

7. Example 1: A B This object is called a “directed graph” – it has nodes and arrows that connect them. How many routes are there from A to B?

8. Example 1: A B How many routes are there from A to B? 1 choice 3 choices 2 choices From the Fundamental Principle of counting, you might guess 1×3×1×2=6, but you would be wrong.

9. Example 1: A B How many routes are there from A to B? 1 choice 3 choices 2 choices AND OR There is a difference between “AND” choices and “OR” choices! You can go by the 1×3×1 = 3 upper paths OR by the 2 lower paths. 3+2 = 5. There are 5 paths.

10. Additive Counting Principle If a task options that DO influence each other (i.e. choosing one item excludes choosing a different item), the total number of choices is m+n+p+… Mutually Exclusive Options

11. To add or multiply? If it is an AND choice, you multiply, if it is an OR choice you add.