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In an examination, there are 5 multiple choice questions with 3 choices, out of which exactly one is correct. There are 3 marks for each correct answer, -2 marks for each wrong answer and 0 mark if the question is not attempted. Then, the number of ways a student appearing in the examination gets 5 marks is _____. (in integer)
Correct answer is '40'. Can you explain this answer?
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Most Upvoted Answer
In an examination, there are 5 multiple choice questions with 3 choice...
Let the student mark x correct answers and y incorrect.
So, 3x - 2y = 5 and x + y 5 where x, y W
The only possible solution is (x, y) = (3, 2).
The student can mark the correct answer by only one choice but for incorrect answer, there are two choices.
So, total number of ways of scoring 5 marks = 5C3(1)3 . (2)2 = 40
So, 3x - 2y = 5 and x + y
≤
∈
The only possible solution is (x, y) = (3, 2).
The student can mark the correct answer by only one choice but for incorrect answer, there are two choices.
So, total number of ways of scoring 5 marks = 5C3(1)3 . (2)2 = 40
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Community Answer
In an examination, there are 5 multiple choice questions with 3 choice...
Given:
- There are 5 multiple-choice questions with 3 choices each.
- Each question has exactly one correct answer.
- Each correct answer is awarded 3 marks.
- Each wrong answer is penalized with -2 marks.
- Not attempting a question gives 0 marks.
To find:
The number of ways a student can score 5 marks.
Approach:
We can solve this problem using combinatorics and by considering all possible combinations.
Solution:
1. Calculate the number of ways to answer correctly:
Since there are 5 questions and each question has 3 choices, the number of ways to answer all questions correctly is 3^5 = 243.
2. Calculate the number of ways to answer incorrectly:
For each question, there are 2 incorrect choices. Therefore, the number of ways to answer all questions incorrectly is 2^5 = 32.
3. Calculate the number of ways to answer partially correct:
To score 5 marks, the student needs to answer all questions correctly. Since each question carries 3 marks, the student needs to answer at least 2 questions correctly. Let's consider the different possibilities:
- Answering 2 questions correctly: The student can choose any 2 questions out of 5 to answer correctly. The number of ways is given by the combination formula, C(5,2) = 5! / (2!(5-2)!) = 10.
- Answering 3 questions correctly: The student can choose any 3 questions out of 5 to answer correctly. The number of ways is given by C(5,3) = 5! / (3!(5-3)!) = 10.
- Answering 4 questions correctly: The student can choose any 4 questions out of 5 to answer correctly. The number of ways is given by C(5,4) = 5! / (4!(5-4)!) = 5.
- Answering all 5 questions correctly: The student can answer all 5 questions correctly in only 1 way.
Therefore, the total number of ways to answer partially correct is 10 + 10 + 5 + 1 = 26.
4. Calculate the number of ways to score 5 marks:
To score 5 marks, the student can either answer all questions correctly, all questions incorrectly, or answer partially correct.
Therefore, the total number of ways to score 5 marks is 243 + 32 + 26 = 301.
However, we need to subtract the cases where the student scores more than 5 marks. This includes cases where the student answers all questions correctly (3^5 = 243) and cases where the student answers more than 2 questions correctly (10 + 10 + 5 = 25).
Therefore, the final number of ways to score 5 marks is 301 - 243 - 25 = 33.
Conclusion:
The number of ways a student appearing in the examination can score 5 marks is 33.
- There are 5 multiple-choice questions with 3 choices each.
- Each question has exactly one correct answer.
- Each correct answer is awarded 3 marks.
- Each wrong answer is penalized with -2 marks.
- Not attempting a question gives 0 marks.
To find:
The number of ways a student can score 5 marks.
Approach:
We can solve this problem using combinatorics and by considering all possible combinations.
Solution:
1. Calculate the number of ways to answer correctly:
Since there are 5 questions and each question has 3 choices, the number of ways to answer all questions correctly is 3^5 = 243.
2. Calculate the number of ways to answer incorrectly:
For each question, there are 2 incorrect choices. Therefore, the number of ways to answer all questions incorrectly is 2^5 = 32.
3. Calculate the number of ways to answer partially correct:
To score 5 marks, the student needs to answer all questions correctly. Since each question carries 3 marks, the student needs to answer at least 2 questions correctly. Let's consider the different possibilities:
- Answering 2 questions correctly: The student can choose any 2 questions out of 5 to answer correctly. The number of ways is given by the combination formula, C(5,2) = 5! / (2!(5-2)!) = 10.
- Answering 3 questions correctly: The student can choose any 3 questions out of 5 to answer correctly. The number of ways is given by C(5,3) = 5! / (3!(5-3)!) = 10.
- Answering 4 questions correctly: The student can choose any 4 questions out of 5 to answer correctly. The number of ways is given by C(5,4) = 5! / (4!(5-4)!) = 5.
- Answering all 5 questions correctly: The student can answer all 5 questions correctly in only 1 way.
Therefore, the total number of ways to answer partially correct is 10 + 10 + 5 + 1 = 26.
4. Calculate the number of ways to score 5 marks:
To score 5 marks, the student can either answer all questions correctly, all questions incorrectly, or answer partially correct.
Therefore, the total number of ways to score 5 marks is 243 + 32 + 26 = 301.
However, we need to subtract the cases where the student scores more than 5 marks. This includes cases where the student answers all questions correctly (3^5 = 243) and cases where the student answers more than 2 questions correctly (10 + 10 + 5 = 25).
Therefore, the final number of ways to score 5 marks is 301 - 243 - 25 = 33.
Conclusion:
The number of ways a student appearing in the examination can score 5 marks is 33.
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In an examination, there are 5 multiple choice questions with 3 choices, out of which exactly one is correct. There are 3 marks for each correct answer, -2 marks for each wrong answer and 0 mark if the question is not attempted. Then, the number of ways a student appearing in the examination gets 5 marks is _____. (in integer)Correct answer is '40'. Can you explain this answer?
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