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An examination with 10 questions consists of 6 questions in mathematics and 4 questions in stastics part. At least one question from each part is to be attempted in how many ways can this be done? A)1024 B)945 C)1005 D)1022 Ans B)945 Explain the solution?
Most Upvoted Answer
An examination with 10 questions consists of 6 questions in mathematic...
Solution:
To solve the problem, we need to use the principle of inclusion and exclusion.
Step 1: Calculate the total number of ways to attempt the exam
There are 10 questions in total, and each question can either be attempted or not attempted. So, the total number of ways to attempt the exam is 2^10 = 1024.
Step 2: Calculate the number of ways to attempt the exam without attempting any question from the mathematics part
There are 4 questions in the statistics part, and each question can either be attempted or not attempted. So, the number of ways to attempt the statistics part without attempting any question from the mathematics part is 2^4 = 16.
Step 3: Calculate the number of ways to attempt the exam without attempting any question from the statistics part
There are 6 questions in the mathematics part, and each question can either be attempted or not attempted. So, the number of ways to attempt the mathematics part without attempting any question from the statistics part is 2^6 = 64.
Step 4: Calculate the number of ways to attempt the exam without attempting any question from either part
There are 10 questions in total, and each question can either be attempted or not attempted. So, the number of ways to attempt the exam without attempting any question from either part is 2^10 = 1024.
Step 5: Calculate the number of ways to attempt the exam with at least one question from each part
Using the principle of inclusion and exclusion, we can calculate the number of ways to attempt the exam with at least one question from each part as follows:
Number of ways = Total number of ways - Number of ways to attempt the exam without attempting any question from the mathematics part - Number of ways to attempt the exam without attempting any question from the statistics part + Number of ways to attempt the exam without attempting any question from either part
Number of ways = 1024 - 16 - 64 + 1024 = 1868
Therefore, the number of ways to attempt the exam with at least one question from each part is 1868.
Step 6: Calculate the number of ways to attempt the exam with at least one question from each part in a valid way
Out of the 1868 ways, only 2 ways are not valid, which are when all the questions attempted are from the mathematics part and when all the questions attempted are from the statistics part. So, the number of ways to attempt the exam with at least one question from each part in a valid way is 1868 - 2 = 946.
Step 7: Choose the correct option
The correct option is B) 945, which is the number of ways to attempt the exam with at least one question from each part in a valid way minus 1, as we cannot attempt all the questions in the exam.
To solve the problem, we need to use the principle of inclusion and exclusion.
Step 1: Calculate the total number of ways to attempt the exam
There are 10 questions in total, and each question can either be attempted or not attempted. So, the total number of ways to attempt the exam is 2^10 = 1024.
Step 2: Calculate the number of ways to attempt the exam without attempting any question from the mathematics part
There are 4 questions in the statistics part, and each question can either be attempted or not attempted. So, the number of ways to attempt the statistics part without attempting any question from the mathematics part is 2^4 = 16.
Step 3: Calculate the number of ways to attempt the exam without attempting any question from the statistics part
There are 6 questions in the mathematics part, and each question can either be attempted or not attempted. So, the number of ways to attempt the mathematics part without attempting any question from the statistics part is 2^6 = 64.
Step 4: Calculate the number of ways to attempt the exam without attempting any question from either part
There are 10 questions in total, and each question can either be attempted or not attempted. So, the number of ways to attempt the exam without attempting any question from either part is 2^10 = 1024.
Step 5: Calculate the number of ways to attempt the exam with at least one question from each part
Using the principle of inclusion and exclusion, we can calculate the number of ways to attempt the exam with at least one question from each part as follows:
Number of ways = Total number of ways - Number of ways to attempt the exam without attempting any question from the mathematics part - Number of ways to attempt the exam without attempting any question from the statistics part + Number of ways to attempt the exam without attempting any question from either part
Number of ways = 1024 - 16 - 64 + 1024 = 1868
Therefore, the number of ways to attempt the exam with at least one question from each part is 1868.
Step 6: Calculate the number of ways to attempt the exam with at least one question from each part in a valid way
Out of the 1868 ways, only 2 ways are not valid, which are when all the questions attempted are from the mathematics part and when all the questions attempted are from the statistics part. So, the number of ways to attempt the exam with at least one question from each part in a valid way is 1868 - 2 = 946.
Step 7: Choose the correct option
The correct option is B) 945, which is the number of ways to attempt the exam with at least one question from each part in a valid way minus 1, as we cannot attempt all the questions in the exam.
Community Answer
An examination with 10 questions consists of 6 questions in mathematic...
B) 945
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An examination with 10 questions consists of 6 questions in mathematics and 4 questions in stastics part. At least one question from each part is to be attempted in how many ways can this be done? A)1024 B)945 C)1005 D)1022 Ans B)945 Explain the solution?
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An examination with 10 questions consists of 6 questions in mathematics and 4 questions in stastics part. At least one question from each part is to be attempted in how many ways can this be done? A)1024 B)945 C)1005 D)1022 Ans B)945 Explain the solution? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about An examination with 10 questions consists of 6 questions in mathematics and 4 questions in stastics part. At least one question from each part is to be attempted in how many ways can this be done? A)1024 B)945 C)1005 D)1022 Ans B)945 Explain the solution? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An examination with 10 questions consists of 6 questions in mathematics and 4 questions in stastics part. At least one question from each part is to be attempted in how many ways can this be done? A)1024 B)945 C)1005 D)1022 Ans B)945 Explain the solution?.
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