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 t

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 _____

TestHub · Accepted Answer

Let the marks obtained in each of the five MCQ be $x_{1}, x_{2}, x_{3}, x_{4}, x_{5}$

Now, $x_{1} + x_{2} + x_{3} + x_{4} + x_{5} = 5$

Only one possibility satisfies the above equation i.e. $3, 3, 3, - 2, - 2$

Hence, total number of ways $= \frac{5!}{3! 2!} \times 2 \times 2 = 40$

Mathematics - Permutation Combination Question with Solution | TestHub

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