Quizzes about the product rule

Product Rule in Combinatorics

Question 1: An economist is analyzing consumer choices between different brands of a product. There are 3 brands of smartphones, 4 brands of laptops, and 2 brands of tablets. How many different combinations of one smartphone, one laptop, and one tablet can a consumer choose?

A. 9
B. 18
C. 24
D. 36

Answer: D. 24

Explanation: According to the product rule: .

Question 2: A market research company offers surveys with different question formats. They have 5 different types of multiple-choice questions, 3 different types of rating scale questions, and 2 different types of open-ended questions. How many unique surveys can be created by choosing one question of each type?

A. 10
B. 15
C. 25
D. 30

Answer: D. 30

Explanation: According to the product rule: .

Product Rule in Engineering

Question 1: An engineering team needs to design a system that uses different components. They can choose from 4 types of sensors, 3 types of processors, and 5 types of power sources. How many different system designs are possible?

A. 30
B. 40
C. 50
D. 60

Answer: D. 60

Explanation: According to the product rule: .

Question 2: A car manufacturing company has 6 models of engines, 4 models of transmissions, and 3 types of chassis. How many different car configurations can be created using one of each type?

A. 48
B. 72
C. 36
D. 24

Answer: B. 72

Explanation: According to the product rule: .

Quiz: Product Rule in Biology

Question 1: A geneticist is studying the combinations of traits in plants. There are 3 different flower colors, 4 different leaf shapes, and 2 different stem heights. How many different combinations of traits can be observed?

A. 9
B. 18
C. 24
D. 36

Answer: C. 24

Explanation: According to the product rule: .

Question 2: A biologist is studying the diet of a species. The diet includes 5 types of fruits, 3 types of insects, and 4 types of plants. How many different dietary combinations can be formed with one type of each food category?

A. 40
B. 60
C. 80
D. 100

Answer: B. 60

Explanation: According to the product rule: