Math A

The Counting Principle

 

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

  

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?  

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.

 

The Counting Principle works for two or more activities.  

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

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

 

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

 

 

 

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Roberts