College Algebra & Trigonometry, 2018a

7.1. THE FUNDAMENTAL PRINCIPLE OF COUNTING 307
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2
All of the possibilities are listed out and can be constructed from the tree diagram.
Here are some sample problems for using the fundamental principle of counting
(also known as the multiplication principle).
Example:
An ice cream shop offers Vanilla, Chocolate, Strawberry, Boysenberry and Rocky
Road ice cream. The ice cream comes with either a waffle cone, a sugar cone or
a wafer cone and can be plain or with sprinkles. How many different ways are
there to order a single scoop of ice cream?
With 5 different types of ice cream, 3 different cones and 2 choices for sprinkles,
there would be 5 ∗ 3 ∗ 2=30different possibilities.