A question paper consists of four questions, each having two possible answers, YES or NO. In how many different ways can a studen…

Question

A question paper consists of four questions, each having two possible answers, YES or NO.

In how many different ways can a student answer at least one question?

1. A. 81
2. B. 16
3. C. 15
4. D. 80 (Correct answer)

Correct Answer

Option D — 80

Detailed Solution & Explanation

The correct answer is 80.

Key Points

• For each question a student may answer YES, answer NO, or leave it unattempted — 3 possibilities per question.
• With four independent questions that gives 3⁴ = 81 total patterns.
• Exactly one of these leaves every question unattempted, and it must be excluded because at least one question is to be answered.
• So the count = 81 − 1 = 80.

Additional Information

• The distractor 16 (= 2⁴) counts only fully-attempted papers; 15 subtracts one from that, and 81 forgets to exclude the blank paper.
• The phrase *at least one* almost always signals the complement method: count everything, then remove the single 'none' case.

*Ministry of Papers worked solution. The Commission has not yet published the official key for this paper; this answer will be reconciled with it on release.*