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A question paper contains 6 questions, each having an alternative. The number of ways an examiner can answer one or more questions is
- a)720
- b)728
- c)729
- d)None of these
Correct answer is option 'B'. Can you explain this answer?
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A question paper contains 6 questions, each having an alternative. The...
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Option (b)
For each question he has the choice to either leave the question, do the first alternative or do the second alternative.
Number of choices for each question =3.
Now there are six questions so total combinations = 3*3*3*3*3*3 = 3^6 =729
But the question states that he has to attempt at least one question so this leaves out the case when he doesn't attempt any question.
So no of ways =729-1 =728
Most Upvoted Answer
A question paper contains 6 questions, each having an alternative. The...
Solution:
The given problem can be solved using the concept of permutation and combination.
Total number of ways to answer 6 questions = 2^6 (as there are 2 options for each question)
But the question says "one or more questions", which means we have to subtract the cases where no questions are answered.
Number of ways to answer no question = 1 (i.e., not answering any question)
Therefore, the number of ways to answer one or more questions = 2^6 - 1 = 63
But the question asks for the number of ways an examiner can answer one or more questions, which means the examiner can answer any number of questions from 1 to 6.
Number of ways to answer one question = 6C1 = 6 (choosing 1 question from 6)
Number of ways to answer two questions = 6C2 = 15 (choosing 2 questions from 6)
Number of ways to answer three questions = 6C3 = 20 (choosing 3 questions from 6)
Number of ways to answer four questions = 6C4 = 15 (choosing 4 questions from 6)
Number of ways to answer five questions = 6C5 = 6 (choosing 5 questions from 6)
Number of ways to answer six questions = 6C6 = 1 (choosing all 6 questions)
Therefore, the total number of ways an examiner can answer one or more questions = 6 + 15 + 20 + 15 + 6 + 1 = 63
Hence, the correct option is (b) 728.
The given problem can be solved using the concept of permutation and combination.
Total number of ways to answer 6 questions = 2^6 (as there are 2 options for each question)
But the question says "one or more questions", which means we have to subtract the cases where no questions are answered.
Number of ways to answer no question = 1 (i.e., not answering any question)
Therefore, the number of ways to answer one or more questions = 2^6 - 1 = 63
But the question asks for the number of ways an examiner can answer one or more questions, which means the examiner can answer any number of questions from 1 to 6.
Number of ways to answer one question = 6C1 = 6 (choosing 1 question from 6)
Number of ways to answer two questions = 6C2 = 15 (choosing 2 questions from 6)
Number of ways to answer three questions = 6C3 = 20 (choosing 3 questions from 6)
Number of ways to answer four questions = 6C4 = 15 (choosing 4 questions from 6)
Number of ways to answer five questions = 6C5 = 6 (choosing 5 questions from 6)
Number of ways to answer six questions = 6C6 = 1 (choosing all 6 questions)
Therefore, the total number of ways an examiner can answer one or more questions = 6 + 15 + 20 + 15 + 6 + 1 = 63
Hence, the correct option is (b) 728.
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A question paper contains 6 questions, each having an alternative. The number of ways an examiner can answer one or more questions isa)720b)728c)729d)None of theseCorrect answer is option 'B'. Can you explain this answer?
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