In part A there are 4 multiple A test requires that you answer either part A or part B. choice questions with 5 possible responses. Part B consists of 6 multiple choice questions with 4 possible responses. How many different answer sheets are possible?
In part A there are 4 multiple A test requires that you answer either part A or part B. choice questions with 5 possible responses. Part B consists of 6 multiple choice questions with 4 possible responses. How many different answer sheets are possible?
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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![**Problem Statement:**
A test requires that you answer either part A or part B. In part A, there are 4 multiple choice questions with 5 possible responses. Part B consists of 6 multiple choice questions with 4 possible responses. How many different answer sheets are possible?
**Explanation:**
To solve this problem, you'll need to calculate the number of different ways you can respond to each part separately and then combine the results.
1. **Part A Calculation:**
- Number of questions: 4
- Responses per question: 5
- Total combinations for Part A: \(5^4 = 625\)
2. **Part B Calculation:**
- Number of questions: 6
- Responses per question: 4
- Total combinations for Part B: \(4^6 = 4096\)
**Total Possible Answer Sheets:**
Since you can choose to answer either Part A or Part B, the total number of different answer sheets is the sum of the combinations for each part:
\[
625 \ (Part \ A) + 4096 \ (Part \ B) = 4721
\]
Therefore, there are 4721 different possible answer sheets.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb83496cd-9baf-4218-91af-6a9eb71001cb%2F757ceea4-5cb0-454a-8ba9-8ed288759536%2Fnn26z6u_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
A test requires that you answer either part A or part B. In part A, there are 4 multiple choice questions with 5 possible responses. Part B consists of 6 multiple choice questions with 4 possible responses. How many different answer sheets are possible?
**Explanation:**
To solve this problem, you'll need to calculate the number of different ways you can respond to each part separately and then combine the results.
1. **Part A Calculation:**
- Number of questions: 4
- Responses per question: 5
- Total combinations for Part A: \(5^4 = 625\)
2. **Part B Calculation:**
- Number of questions: 6
- Responses per question: 4
- Total combinations for Part B: \(4^6 = 4096\)
**Total Possible Answer Sheets:**
Since you can choose to answer either Part A or Part B, the total number of different answer sheets is the sum of the combinations for each part:
\[
625 \ (Part \ A) + 4096 \ (Part \ B) = 4721
\]
Therefore, there are 4721 different possible answer sheets.
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