Fundamental Principles of Counting

The Fundamental Counting Principle allows you to...

• see each and every possible outcome possibility in your sample.

• find the number of total outcomes in your sample.

• count how many times you must do a tree diagram.

• see how many outcomes will not show up on a tree diagram.

Use the Fundamental Counting Principle to find out how many total outcomes you have:

You are buying a car and have to make the following decisions: (brand: Toyota, Honda, Ford), (color: Red, Green, Blue, Black, Silver), (transmission: Manual or Automatic)

• 10

• 3

• 30

• 72

Use the Fundamental Counting Principle to find out how many total outcomes you have:

You go to an ice cream shop and get to choose: (flavor: Chocolate, Vanilla, Strawberry, Swirl), (scoops: 1, 2, or 3), (toppings: Sprinkles, Gummi Bears, Nerds, Chocolate Chips), and (cone: Waffle or Sugar).

• 96

• 4

• 14

• 240

Use the Fundamental Counting Principle to find out how many total outcomes you have:

You go to an entertainment center and get to pick how to spend the day with friends: (activity 1: go-karts, bowling, mini golf), (food: hot dogs, corn dogs, hamburgers, pizza), and (activity 2: laser tag, arcade, skating)

• 80

• 10

• 3

• 36

Use the Fundamental Counting Principle to find out how many total outcomes you have:

You toss 4 coins: (coin 1: H or T), (coin 2 : H or T), (coin 3 (H or T), and (coin 4: H or T)

• 8

• 81

• 16

• 4

Use the Fundamental Counting Principle to find out how many total outcomes you have:

You roll 2 dice and flip 3 coins: (die 1: 1, 2, 3, 4, 5, 6), (die 2: 1, 2, 3, 4, 5, 6), (coin 1: H or T), (coin 2: H or T), and (coin 3: H or T)

• 18

• 288

• 392

• 5

You are buying a car and have to make the following decisions: (brand: Toyota, Honda, Ford), (color: Red, Green, Blue, Black, Silver), (transmission: Manual or Automatic).

What is the probability of buying a Toyota (brand) in Blue or Red (color) with Manual drive (transmission)? (Hint: You can still use the Fundamental Counting Principle to find your numerator (what you want to buy) and then your denominator (your original choices.)

You roll 2 dice and flip 3 coins: (die 1: 1, 2, 3, 4, 5, 6), (die 2: 1, 2, 3, 4, 5, 6), (coin 1: H or T), (coin 2: H or T), and (coin 3: H or T).

What is the probability of rolling an EVEN number on the first die, an ODD number on the second die, and all HEADS for the three coins? (Hint: You can still use the Fundamental Counting Principle to find your numerator (what you want to buy) and then your denominator (your original choices.)

You go to an entertainment center and get to pick how to spend the day with friends: (activity 1: go-karts, bowling, mini golf), (food: hot dogs, corn dogs, hamburgers, pizza), and (activity 2: laser tag, arcade, skating). 

What is the probability of selecting to go-kart, eat ANY of the four food options, and ending the day with laser tag? (Hint: You can still use the Fundamental Counting Principle to find your numerator (what you want to buy) and then your denominator (your original choices.)

You go to an ice cream shop and get to choose: (flavor: Chocolate, Vanilla, Strawberry, Swirl), (scoops: 1, 2, or 3), (toppings: Sprinkles, Gummi Bears, Nerds, Chocolate Chips), and (cone: Waffle or Sugar). 

What is the probability of buying a Swirl, Two-scoop ice cream with Chocolate Chips on a Waffle Cone? (Hint: You can still use the Fundamental Counting Principle to find your numerator (what you want to buy) and then your denominator (your original choices.)