Final answer:
To calculate the total ways a student can complete the quiz, we multiply the number of ways to answer each type of question. There are 2^3 (8) ways for true-or-false and 4^2 (16) ways for multiple choice questions, resulting in a total of 128 ways to complete the quiz.
Step-by-step explanation:
The question is asking how many ways a student can complete a quiz that consists of 3 true-or-false questions and 2 multiple choice questions with 4 options each. To find the number of different ways the quiz can be completed, we use the fundamental counting principle which states that if there are n ways to do something and m ways to do another thing, then there are n × m ways to perform both actions.
- For each true-or-false question, there are 2 possible answers (true or false).
- For each multiple choice question, there are 4 possible answers.
Using the counting principle:
- The number of ways to answer the true-or-false questions is 2 × 2 × 2 = 2^3 = 8 ways.
- The number of ways to answer the multiple choice questions is 4 × 4 = 4^2 = 16 ways.
- To find the total number of ways to complete the quiz, we multiply the number of ways to answer the true-or-false questions by the number of ways to answer the multiple choice questions, which gives us 8 × 16 = 128 ways to complete the quiz.
Therefore, there are 128 different ways for a student to complete this quiz.