Problem 33 - Algebra and Trigonometry

Question

You are taking a multiple-choice test that has five questions. Each of the questions has three answer choices, with one correct answer per question. If you select one of these three choices for each question and leave nothing blank, in how many ways can you answer the questions?

Step-by-Step Solution

Answer

There are 243 different ways to answer the questions.

Step 1: Analyze the number of choices per question

Observe that each question has three answer choices. Therefore, there are 3 ways to answer each individual question.

Step 2: Apply multiplication principle

Since the selection of options for each question is independent from the others, the total number of ways to answer all questions is equivalent to the multiplication of number of ways to answer each question. The multiplication principle states that if one event can occur in m ways, a second can occur independently in n ways, then the two events can occur in m*n ways.

Step 3: Calculate total number of ways to answer all questions

There are 5 questions in total, hence you can answer all questions in \(3^5 = 243\) ways.