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Worksheet: 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?

  • A 11
  • B 17
  • C 21
  • D 42
  • E 187

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 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 , 3 , 2 } . Given that he currently knows nothing about the other digits, how many possible numbers does he have left to try?

Q4:

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?

Q5:

A cafe offers a choice of 20 meals and 12 beverages. In how many different ways can a person choose a meal and a beverage?

Q6:

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.

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:

There are 6 books left in a store. In how many ways can 5 people take one book each?

  • A360
  • B6
  • C 2 520
  • D720
  • E30

Q9:

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?

Q10:

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.

  • A 59
  • B 87
  • C 27
  • D 1 022
  • E 5 133

Q11:

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

Q12:

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

Q13:

How many four-digit numbers, with no repeated digits, can be formed using the elements of the set { 1 , 2 , 3 , 7 , 9 } ?

Q14:

Determine the number of ways of selecting 2 teachers from 19.

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:

Determine the number of ways of selecting a letter from the set of letters { , , , , , , } v w x y z a b .

Q17:

In a town, there are 9 hotels. In how many ways can three tourists stay in the town, given they each want to stay in a different hotel?

Q18:

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.

Q19:

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.

  • A8
  • B10
  • C20
  • D16
  • E12

Q20:

In how many ways can we pick 5 different letters from the English alphabet?

Q21:

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.

Q22:

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.

Q23:

If there were 83 men and 12 women in a town, in how many ways could a committee which consists of one man and one woman be formed?

Q24:

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 ?

Q25:

Suppose 10 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.