Question

In an examination, there are three multiple choice questions and each question has $4$ choices. Number of ways in which a student can fail to get all answers correct is

• A. $11$
• B. $12$
• C. $27$
• D. $63$

Answer 1

Answer: (D)

$63$

Answer 2

There are three multiple choice questions, each has four possible answers. Therefore, the total number of possible answers will be $4 \times 4 \times 4 = 64$. Out of these possible answers only one will be correct and hence the number of ways in which a student can fail to get all correct answers is $64 - 1 = 63$.