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Video: Application of the Counting Principle (Product Rule)

Tim Burnham

An ice cream shop offers 3 different cup sizes and 14 flavours. How many ways are there to buy a single flavour of ice cream?

01:07

Video Transcript

An ice cream store offers three different cup sizes and 14 different flavors. How many ways are there to buy a single flavor of ice cream?

Well, my first decision is which size cup. And I got three different sizes; let’s call them small, medium, or large. Now, I’ve got 14 different options for flavors if I choose the small cone, the same 14 different options if I choose the medium cone, and the same 14 different options if I choose the large cone.

So for each flavor, there are three different options for how I buy it. I could have small strawberry, medium strawberry, large strawberry; small chocolate, medium chocolate, large chocolate; small cola, medium cola, large cola.

So however many flavors I’ve got, with three different ways of choosing those flavors, I’ve got three times as many options in terms of how I receive my ice cream. And that’s 42 ways in total to buy a single flavor of ice cream.