Quizzes about the product rule

Question 1: There are 4 different types of shirts and 3 different types of pants. How many different outfits can you make with one shirt and one pair of pants?

A. 7
B. 10
C. 12
D. 15

Show Answer

According to the product rule, the number of outfits is the product of the number of shirts and the number of pants. 4 \times 3 = 12 .

Question 2: A cafeteria offers 5 different types of sandwiches, 4 different types of drinks, and 3 different types of desserts. How many different meal combinations can be made if you choose one sandwich, one drink, and one dessert?

A. 12
B. 20
C. 60
D. 80

Show Answer

Explanation: According to the product rule, the number of meal combinations is the product of the number of sandwiches, drinks, and desserts:

5 \times 4 \times 3 = 60.

Question 1: A password consists of 2 letters followed by 3 digits. How many different passwords can be formed?

A. 26
B. 2600
C. 676000
D. 67600

Show Answer

There are 26 options for each letter and 10 options for each digit. According to the product rule: 26 \times 26 \times 10 \times 10 \times 10 = 67600 .

Question 2: A university offers 3 different types of courses. Each course has 4 different sections, and each section is taught by 2 different professors. How many different ways can a student attend one section of each type of course?

A. 12
B. 24
C. 48
D. 96

Show Answer

According to the product rule: 3 \times 4 \times 2 \times 4 \times 2 \times 4 \times 2 = 96 .

Question 1: An event organizer needs to set up a stage. There are 5 different types of backdrops, 4 different types of lighting setups, and 3 different types of sound systems. Additionally, there are 2 different types of projectors. How many different stage setups can be created?

A. 120
B. 240
C. 480
D. 600

Show Answer

According to the product rule: 5 \times 4 \times 3 \times 2 = 120 .

Question 2: In a coding competition, each contestant needs to solve 3 different types of problems (easy, medium, and hard). There are 5 easy problems, 4 medium problems, and 3 hard problems. How many different ways can a contestant choose one problem of each type?

A. 60
B. 70
C. 80
D. 90

Show Answer

According to the product rule: 5 \times 4 \times 3 = 60 .


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