Q19. - Algebra 2

Question

Each question on a five-question multiple-choice quiz has answer choices labelled A, B, C, and D. How many different ways can a student answer the five questions?

Step-by-Step Solution

Answer

There are 1024 different ways a student can answer the five questions.

Step 1. Given Information.

Given, each question on a five-question multiple-choice quiz has answer choices labelled A, B, C, and D. It is to be determined how many different ways can a student answer the five questions.

Step 2. Calculation .

There are 4 ways to choose among the 4 different answer choices.

And there are 5 questions i.e., each of the 5 question has 4 choices.

 

By the Fundamental Counting Principle, there are $4\times 4\times 4\times 4\times 4=1024$ different ways a student can answer the five questions.

Step 3. Conclusion .

Hence, by Fundamental Counting Principle, there are 1024 different ways a student can answer the five questions.