Worksheet: Fundamental Counting Principle

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 code breaker is trying to find the value of an eight digit number. The figure below shows the digits that he has already discovered. He has narrowed down his options for the digit represented by the letter 𝑐 to the following set of numbers {5,6,4}. Given that he currently knows nothing about the other digits, how many possible numbers does he have left to try?

Q3:

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?

Q4:

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

Q5:

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?

Q6:

Determine the number of ways of selecting a letter from the set of letters {,,,,,,}vwxyzab.

Q7:

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?

Q8:

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.

Q9:

These three spinners are spun. How many unique combinations are there where the first lands on an even number, the second lands on blue or green and the third lands on the letter 𝑂?

Q10:

A skateboard shop stocks 10 types of board decks, 3 types of trucks, and 4 types of wheels. How many different skateboards can be constructed?

Q11:

A password is formed of three different digits from 0–9 and three different lowercase letters from a–z. Determine the total number of possible passwords.

Q12:

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?

Q13:

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.

Q14:

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

Q15:

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

Q16:

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.

Q17:

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.

Q18:

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.

Q19:

James is developing an experiment to represent people choosing from six different flavors of soup. Which of the following would be most useful to help him model the possible outcomes?

  • Aa spinner with 8 sections
  • Ba deck of 52 cards
  • Ca coin
  • Da number cube

Q20:

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.

Q21:

A bag contains 11 balls numbered from 1 to 11. In an experiment, a ball is selected at random from the bag, replaced, and then another ball is selected. How many outcomes are there in which the sum of the numbers on the two chosen balls is more than 17?

Q22:

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?

Q23:

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

Q24:

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

Q25:

Two spinners are spun. The first spinner is numbered from 1 to 7, and the second spinner is numbered from 1 to 8. Using a tree diagram, determine the probability of both spins being the same number.

  • A14 out of 56
  • B8 out of 56
  • C49 out of 56
  • D7 out of 56

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