1. When dealing with the occurrence of more than one event, it is important to be able to quickly determine how many possible outcomes exist.

2. For example, if ice cream sundaes come in 5 flavors with 4 possible toppings, how many different sundaes can be made with one flavor of ice cream and one topping?  

3. Rather than list the entire sample space with all possible combinations of ice cream and toppings, we may simply multiply 5 • 4 = 20 possible sundaes.  This simple multiplication process is known as the Counting Principle.

4. The Counting Principle works for two or more activities.

5. A coin is tossed five times
A coin is tossed five times.  How many arrangements of heads and tails are possible?

6. By the Counting Principle, the sample space (all possible arrangements) will be 2•2•2•2•2 = 32 arrangements of heads and tails.

7. Remember: The Counting Principle is easy
Remember:  The Counting Principle is easy!  Simply MULTIPLY the number of ways each activity can occur.

8. Example 1:
A movie theater sells 3 sizes of popcorn (small, medium, and large) with 3 choices of toppings (no butter, butter, extra butter).  How many possible ways can a bag of popcorn be purchased?

9. Example 2:
Information about girls' ice skates: Colors:  white, beige, pink, yellow, blue Sizes: 4, 5, 6, 7, 8 Extras:  tassels, striped laces, bells Assuming that all skates are sold with ONE extra, how many possible arrangements exist?  

10. Example 3:
Your state issues license plates consisting of letters and numbers.  There are 26 letters and the letters may be repeated.  There are 10 digits and the digits may be repeated.  How many possible license plates can be issued with two letters followed by three numbers?

11. Example 4:
Heather has finally narrowed her clothing choices for the big party down to 3 skirts, 2 tops and 4 pair of shoes.  How many different outfits could she form from these choices?

12. Example 5:
The ice cream shop offers 31 flavors.  You order a double-scoop cone.  In how many different ways can the clerk put the ice cream on the cone if you wanted two different flavors?