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The number of all selections which a student can make for answering one or more questions out of 8 given questions in a paper, when each question has an alternative, is:

  • a)
    6560 

  • b)
    256

  • c)
    255

  • d)
    6561

Correct answer is option 'C'. Can you explain this answer?
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Solution:

Given that there are 8 questions in the paper, and each question has an alternative. The student can choose one or more questions to answer.

To find the total number of selections the student can make, we use the concept of combinations.

The total number of selections is the sum of the number of selections for each possible number of questions answered.

Number of selections for answering 1 question: 8C1 = 8

Number of selections for answering 2 questions: 8C2 = 28

Number of selections for answering 3 questions: 8C3 = 56

Number of selections for answering 4 questions: 8C4 = 70

Number of selections for answering 5 questions: 8C5 = 56

Number of selections for answering 6 questions: 8C6 = 28

Number of selections for answering 7 questions: 8C7 = 8

Number of selections for answering 8 questions: 8C8 = 1

Total number of selections = 8 + 28 + 56 + 70 + 56 + 28 + 8 + 1 = 255.

However, the question also asks for the number of selections when the student can choose to answer one or more questions. This means that the student can choose to answer any number of questions from 1 to 8.

Therefore, we need to add one more selection to the total, which is the selection where the student does not answer any questions.

Total number of selections when the student can choose to answer one or more questions = 255 + 1 = 256.

Hence, the correct answer is option (b) 256.
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The number of all selections which a student can make for answering one or more questions out of 8 given questions in a paper, when each question has an alternative, is:a)6560b)256c)255d)6561Correct answer is option 'C'. Can you explain this answer?
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