In an examination, there are four multiple-choice questions with three options each, of which one option is the correct answer. In how many ways can a student answer such that he fails to answer all four questions correctly?

4 multiple choice questions 3 answers per question
4 × 3 = 12
12 possible answers total
12 - 4 = 8
*8 incorrect answers **4 correct answers **
*3 × 3 × 3 × 3 = 81 *
**81 possible ways they can answer **
*Only one of those ways is 100% correct. *
*81 - 1 = 80
80 ways

Answered by iloveonedirection | 2024-06-10

A student can answer the four multiple-choice questions incorrectly in 80 different ways. This is calculated by taking the total possible responses (81) and subtracting the 1 way to answer all questions correctly. Thus, there are 80 ways to fail to answer all questions correctly.
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Answered by iloveonedirection | 2024-12-26