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

The correct option is D

$63$

Explanation for the correct option:

Finding the number of ways:

Each question has four choices. So, the total number of ways in which the questions can be attempted is $4^3$.

Number of ways of getting all correct is $1^3$.

So, the number of ways of getting all wrong is $4^3-1^3=63$

Hence, option D is correct.