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.

Q1:

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?

Q2:

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.

Q3:

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?

Q4:

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?

Q5:

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?

Q6:

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?

Q7:

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

Q8:

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

Q9:

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.

Q10:

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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