Lesson Worksheet: Fundamental Counting Principle Mathematics

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:

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?

Q3:

Using the fundamental counting principle, determine the number of possible outcomes if the two shown spinners were spun.

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 school gives three prizes for excellence. The short lists for the prizes contain 9 students, 7 students, and 6 students. In how many ways can the prizes be distributed?

Q6:

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.

Q7:

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?

Q8:

A car dealership offers 73 different models of cars and 14 different colors. Determine the number of ways someone can pick a car in a single color.

Q9:

A building has 7 doors labeled 1,2,3,,7. In how many ways can a person enter and then leave the building?

Q10:

How many ways can we pick a team of one man and one woman from a group of 23 men and 14 women?

Q11:

Use the fundamental counting principle to find the total number of outcomes upon choosing a number from 1 to 28 and a vowel from the word COUNTING.

Q12:

A fancy dress store has a selection of 8 pairs of pants and 2 shirts. Determine the number of ways someone can pick a pair of pants and a shirt.

Q13:

Use the fundamental counting principle to determine the total number of outcomes upon choosing from 8 ice cream flavors; small, medium, or large cones; and either caramel or chocolate sauce.

Q14:

Two spinners are spun. The first spinner is numbered from 1 to 5, and the second spinner is numbered from 1 to 7. Determine the total number of possible outcomes.

Q15:

A bag contains 3   balls numbered from 1 to 3. In an experiment, a ball is selected at random from the bag, replaced, and then another ball is selected. How many possible outcomes are there?

Q16:

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

Q17:

Use the fundamental counting principle to find the total number of outcomes of tossing 11 coins.

Q18:

There are 9 ships which travel between two ports. Determine the number of ways to travel from one port to another, and then back again, without using the same ship for both journeys.

Q19:

How many ways can a committee of one man and one woman be formed from 83 men and 12 women?

Q20:

Use the fundamental counting principle to determine the total number of outcomes of choosing a number from 2 to 37 and a book from 14 books.

Q21:

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.

Q22:

Using the fundamental counting principle, determine the total number of outcomes of rolling 9 number cubes.

Q23:

In how many ways can a shirt and a hat be chosen, given 20 shirts and 13 hats to choose from?

Q24:

Use the fundamental counting principle to determine the total number of outcomes of picking out an outfit from 4 shirts, 8 pairs of pants, and 2 jackets.

Q25:

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.

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