In Example 1, all the possibilities for this question have been found. However, an assumption is made in solving the problem - customers are able to order only one of the 20 choices listed in the sample space. Although this assumption is made for the sake of solving the math problem, it is likely that customers could order an ice cream cone with no topping or an ice cream cone with two ice cream flavours. Assumptions are often unavoidable when solving counting problems.

In Example 1, sample space was used to determine the number of possibilities that exist in a given scenario. Imagine that the ice cream store had 3 types of cones, carried 25 types of ice cream, and offered 6 toppings.  

Given this new information, sample space would not be a very efficient method to solve the problem because listing all the possible outcomes would be very time consuming.

In a problem such as this with a large sample space, a method known as the Fundamental Counting Principle is used because it does not require a person to list the possible outcomes to solve the problem. 

You know that the answer to Example 1 was 20 possibilities. To solve this example using the Fundamental Counting Principle, you need to multiply:

 

Now, look at another example of how the Fundamental Counting Principle can be used.