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 ____________.
Answer (integer)
40
Solution
Let student marks $x$ correct answers and $y$ incorrect. So
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$3 x-2 y=5$ and $x+y \leq 5$ where $x, y \in \mathrm{W}$
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Only possible solution is $(x, y)=(3,2)$
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Students can mark correct answers by only one choice but for an incorrect answer, there are two choices. So total number of ways of scoring 5 marks $={ }^{5} C_{3}(1)^{3} \cdot(2)^{2}=40$
About this question
Subject: Mathematics · Chapter: Permutations and Combinations · Topic: Fundamental Counting Principle
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