Q: A license plate consists of 3 letters (A-Z) followed by 3 digits (0-9). How many different license plates are possible?

$$26^3$$ \times $$10^3 = 17$$,576,000$$

Q: You are creating a password that consists of 2 uppercase letters followed by 4 digits. How many different passwords are possible?

$$26^2$$ \times $$10^4 = 676$$ \times 10,000 = 6,760,000$$

Q: A university ID consists of 2 letters followed by 3 digits. How many unique IDs are possible?

$$26^2$$ \times $$10^3 = 676$$ \times 1000 = 676,000$$

Q: A security code consists of 3 letters (A-Z) and 2 digits (0-9). How many different codes are possible?

$$26^3$$ \times $$10^2 = 17$$,576 \times 100 = 1,757,600$$

Q: A code consists of 2 uppercase letters followed by 2 digits, followed by 1 special character (from 5 options). How many different codes are possible?

$$26^2$$ \times $$10^2$$ \times 5 = 676 \times 100 \times 5 = 338,000$$

Q: A password consists of 3 lowercase letters and 3 digits. How many different passwords are possible?

$$26^3$$ \times $$10^3 = 17$$,576 \times 1,000 = 17,576,000$$

Question 1

Suppose you have 5 different shirts and 4 different pairs of pants. According to the Fundamental Counting Principle, how many unique shirt-and-pant outfits can you create?

Accepted Answer

$$5 	imes 4 = 20$$

Question 2

A restaurant offers 3 types of bread, 5 types of meat, and 4 types of cheese for a sandwich. If you must choose one of each, how many different sandwiches are possible?

Accepted Answer

$$3 	imes 5 	imes 4 = 60$$

Question 3

If you roll 5 dice, each with 6 sides, how many possible outcomes are there?

Accepted Answer

$$6^5 = 7776$

Question 4

A license plate consists of 3 letters (A-Z) followed by 3 digits (0-9). How many different license plates are possible?

Accepted Answer

$$26^3$$ 	imes $$10^3 = 17$$,576,000$$

Question 5

A phone number is 10 digits long. If the first digit cannot be 1 or 4, and no digit can be 7, how many possible phone numbers are there?

Accepted Answer

$$8 	imes 9^9$

Question 6

You are creating a password that consists of 2 uppercase letters followed by 4 digits. How many different passwords are possible?

Accepted Answer

$$26^2$$ 	imes $$10^4 = 676$$ 	imes 10,000 = 6,760,000$$

Question 7

A cafeteria offers 4 types of drinks, 3 types of sandwiches, and 2 types of desserts. If you choose one of each, how many meal combinations are possible?

Accepted Answer

$$4 	imes 3 	imes 2 = 24$$

Question 8

A student must choose one science class from 5 options, one math class from 4 options, and one history class from 3 options. How many different ways can the student choose their classes?

Accepted Answer

$$5 	imes 4 	imes 3 = 60$$

Question 9

A lock has a 4-digit code, where each digit can be any number from 0 to 9. How many possible codes are there?

Accepted Answer

$$10^4 = 10$$,000$$

Question 10

A school is forming a committee with one student from each of 6 different classes. If each class has 5 students, how many different committees are possible?

Accepted Answer

$$5^6 = 15$$,625$$

Question 11

A pizza shop offers 3 types of crust, 4 types of cheese, and 5 types of toppings. If you choose one of each, how many different pizzas can you order?

Accepted Answer

$$3 	imes 4 	imes 5 = 60$$

Question 12

A university ID consists of 2 letters followed by 3 digits. How many unique IDs are possible?

Accepted Answer

$$26^2$$ 	imes $$10^3 = 676$$ 	imes 1000 = 676,000$$

Question 13

A password must be 6 characters long, each character can be a digit (0-9) or a lowercase letter (a-z). How many possible passwords are there?

Accepted Answer

$$36^6$$

Question 14

A car rental company offers 4 types of cars, 3 colors, and 2 insurance packages. How many different rental options are available?

Accepted Answer

$$4 	imes 3 	imes 2 = 24$$

Question 15

A student is choosing a meal with 2 appetizers, 3 main courses, and 2 desserts. If they must choose one of each, how many possible meal combinations are there?

Accepted Answer

$$2 	imes 3 	imes 2 = 12$$

Question 16

A security code consists of 3 letters (A-Z) and 2 digits (0-9). How many different codes are possible?

Accepted Answer

$$26^3$$ 	imes $$10^2 = 17$$,576 	imes 100 = 1,757,600$$

Question 17

A student must select one book from each of 4 different genres. If each genre has 6 books, how many ways can the student select one book from each genre?

Accepted Answer

$$6^4 = 1296$

Question 18

A code consists of 2 uppercase letters followed by 2 digits, followed by 1 special character (from 5 options). How many different codes are possible?

Accepted Answer

$$26^2$$ 	imes $$10^2$$ 	imes 5 = 676 	imes 100 	imes 5 = 338,000$$

Question 19

A student is creating a schedule by choosing one class from each of 5 periods. If each period has 4 class options, how many possible schedules are there?

Accepted Answer

$$4^5 = 1024$

Question 20

A password consists of 3 lowercase letters and 3 digits. How many different passwords are possible?

Accepted Answer

$$26^3$$ 	imes $$10^3 = 17$$,576 	imes 1,000 = 17,576,000$$

Fundamental Counting Principle in Probability and Statistics

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