A teacher gave a quiz consisting of 5 item matching test and a 5 item multiple choice with 4 choices each. If a student answer each question in the quiz, in how many ways can you answer the question?
For the first part, there are 5 items to match and 5 choices. We can choose the first item in 5 ways, then the second item in 4 ways (since one choice has already been used), then the third item in 3 ways, then the fourth item in 2 ways, and the last item in 1 way. So the total number of ways to match the items is:
5 x 4 x 3 x 2 x 1 = 120
For the second part, there are 5 multiple choice questions with 4 choices each. For each question, we can choose one of the 4 choices, so the total number of ways to answer the multiple choice questions is:
4 x 4 x 4 x 4 x 4 = 4^5 = 1024
To find the total number of ways to answer the entire quiz, we multiply the number of ways to answer the matching questions by the number of ways to answer the multiple choice questions:
120 x 1024 = 122,880
Therefore, there are 122,880 ways to answer the quiz.
Answers & Comments
Answer:
122,880
Step-by-step explanation:
For the first part, there are 5 items to match and 5 choices. We can choose the first item in 5 ways, then the second item in 4 ways (since one choice has already been used), then the third item in 3 ways, then the fourth item in 2 ways, and the last item in 1 way. So the total number of ways to match the items is:
5 x 4 x 3 x 2 x 1 = 120
For the second part, there are 5 multiple choice questions with 4 choices each. For each question, we can choose one of the 4 choices, so the total number of ways to answer the multiple choice questions is:
4 x 4 x 4 x 4 x 4 = 4^5 = 1024
To find the total number of ways to answer the entire quiz, we multiply the number of ways to answer the matching questions by the number of ways to answer the multiple choice questions:
120 x 1024 = 122,880
Therefore, there are 122,880 ways to answer the quiz.