Question

In an examination, there are 5 multiple choice questions with 3 choices, out of which exactly one is correct. There are 3 marks for each correct answer, −2 marks for each wrong answer and 0 mark if the question is not attempted. Then, the number of ways a student appearing in the examination gets 5 marks is

A. 40
B. 40.00
C. 40.0

Answer 1

There are 40 ways for a student to get 5 marks in the exam and the correct option is A.

There are 3 marks for each correct answer, -2 marks for each wrong answer and 0 mark if the question is not attempted.

Then, the number of ways a student appearing in the examination gets 5 marks is

Solution:

For each question, the marks are 3 for correct and −2 for wrong.

For getting 5 marks, the student has to answer 5 correct and 0 wrong.

The number of ways of answering 5 correct and 0 wrong is 5C3⋅(1)3⋅(2)2=10⋅1⋅4=40

Hence, the number of ways a student appearing in the examination gets 5 marks is 40.

So the answer is A. 40