Lesson Worksheet: Fundamental Counting Principle Mathematics • 12th Grade

In this worksheet, we will practice finding the number of all possible outcomes in a sample space using the fundamental counting principle.


An ice cream store offers 3 different cup sizes and 14 flavors. How many ways are there to buy a single flavor of ice cream?


Suppose 4 fair coins are tossed at the same time that these two spinners are spun. Using the fundamental counting principle, find the total number of possible outcomes.


Michel, Kayla, and ChiWei are playing a game, where one of them needs to be a sheriff and one needs to be an outlaw. They write each of their names on a piece of paper and place them in a bowl. If two names are picked at random where the first will be a sheriff and the second will be an outlaw how many different ways are there?


A cafe offers a choice of 20 meals and 9 beverages. In how many different ways can a person choose a meal and a beverage?


A construction company currently has three active sites. There are 20 different ways to drive from site 𝐴 to site 𝐵. There are 16 ways to drive from site 𝐵 to site 𝐶. In how many ways can we drive from site 𝐴 to site 𝐶 visiting site 𝐵 on the way?


A restaurant serves 2 types of pie, 4 types of salad, and 3 types of drink. How many different meals can the restaurant offer if a meal includes one pie, one salad, and one drink?


In how many ways can a 5-digit code be formed using the numbers 1 to 9? Note, the code can have repeated digits.


Use the fundamental counting principle to find the total number of outcomes of rolling 4 number cubes and tossing 2 coins.


Use the fundamental counting principle to determine the total number of outcomes of choosing (with the possibility of repetition) a password that begins with three letters followed by three numbers from 1 to 7. Assume the password can only contain lower case letters.


In a small town, there are 4 paths connecting the library and the post office, 5 paths connecting the post office and the bank, and 2 paths connecting the bank and the park. Determine the number of ways to walk from the library to the park.

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