A test has four questions: The first question is a true/false question, and it is followed by three multiple choice questions (answers a, b, c, d).
a. How many different ways can this test be answered if each question is answered?
There are 2 ways to answer the true/false question (true or false), and 4 ways to answer each of the multiple choice questions (a, b, c, or d). Therefore, the total number of ways to answer the entire test is:
2 * 4 * 4 * 4 = 128
So there are 128 different ways to answer the test if each question is answered.
To calculate the number of different ways this test can be answered, we need to consider the possibilities for each question.
1. True/False Question:
There are 2 possible answers for this question (True or False).
2. Multiple Choice Questions:
For each multiple choice question, there are 4 possible answers (a, b, c, d). Since there are three multiple-choice questions, we have 4 options for each question.
To find the total number of different ways this test can be answered, we multiply the possibilities for each question as follows:
Total ways = (Possibilities for 1st question) x (Possibilities for 2nd question) x (Possibilities for 3rd question) x (Possibilities for 4th question)
Total ways = 2 (for true/false) x 4 (for 1st multiple-choice question) x 4 (for 2nd multiple-choice question) x 4 (for 3rd multiple-choice question)
Therefore, there are 2 x 4 x 4 x 4 = 128 different ways this test can be answered.