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Lesson: Fundamental Counting Principle

Sample Question Videos

Worksheet • 25 Questions • 3 Videos


An ice cream shop offers 3 different cup sizes and 14 flavours. How many ways are there to buy a single flavour of ice cream?


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?


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?


Determine the number of ways a committee of 7 people, consisting of 5 boys and 2 girls, can be formed from a group of 9 boys and 4 girls.


Using the Fundamental Counting Principle, determine the number of all possible outcomes if the two shown spinners were spun.


Maged must create a password for his new computer. The password is not case sensitive and consists of 4 English letters. Determine how many different passwords can be created if letters cannot be repeated.


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?


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


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?


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.


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 ?


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?


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.


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?


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


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


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


How many four-digit numbers can be formed using the elements of the set { 1 , 2 , 3 , 7 , 9 } ?


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


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


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?


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.


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


In how many ways can we make 5 different words from the English alphabet?


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.