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A test consists of five multiple-choice questions, each of which has three alternative solutions—but only one of them is correct. Three points are awarded for each correctly answered question, two points for each incorrect one, and no points are awarded if the question is not even attempted. Thus, there are _________ possible methods for a test-taking student to achieve a score of 5. 

 

Option: 1

40


Option: 2

45


Option: 3

50


Option: 4

55


Answers (1)

best_answer

The student receives a score of 5 .
Then if \mathrm{x} is the number of correct answers and \mathrm{y} is the number of incorrect answers

Then 3 x-2 y=5
Where x+y \leq 5

The possible solutions for (x, y) \varepsilon(3,2)

For a given question
There is only one way to mark the correct answer, but there are two ways to mark an incorrect answer.

Then the ways will be ={ }^{5} C_{3} \cdot(1)^{3} \cdot(2)^{2}
                                    =40

The correct option is (a).

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