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 answer correct is?

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

Answer 1

Answer: (D)

$63$

There are 4 choices for each question. So, there

are 4 ways to answer a question.

Number of ways to answer 3 questions

$=4\times 4\times 4$

$\downarrow$ $\downarrow$ $\downarrow$

$1^{st}$ question $2^{nd}$ $3^{rd}$

$=64$

Out of 64 ways there is only one way which has

all the answers correct.

So, Number of ways in which a student can fail to get all answers

correct $=64-1$

$=63$