Question

In an examination there are three multiple choice questions and each question has $4$ choices out of which only one is correct. If all the questions are compulsory, then 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)

$63$

3 questions have four choice each.

Total no. of ways of ans wrong = ${}^4{C}_1{\times }^4{C}_1{\times }^4{C}_1$

$=4\times 4\times 4$

$=64$ ways

$\therefore$ Number of ways the student fails b get all

current = [ total number of ways hecan answer]-

[no. of ways he get all the question correct]

no. of ways he get all the correct = 1 way

($\therefore$ there are definite answere to each question)

No. of ways student fails toget all correct $=64-1=63$

$answer=63$