Question

In an examination there are four multiple choice questions with 3 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 the four questions correctly? Thank you for help :)

Answer 1

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