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.

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)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

x 1+ x 2+ x 3+ x 4+ x 5=5 Only one possibilities 3,3,3,-2,-2 Number of ways is =(5 !/3 ! 2 !) × 2 × 2=40

x1​+x2​+x3​+x4​+x5​=5 Only one possibilities 3,3,3,−2,−2 Number of ways is =3!2!5!​×2×2=40

$x_{1} + x_{2} + x_{3} + x_{4} + x_{5} = 5$
Only one possibilities $3, 3, 3, - 2, - 2$
Number of ways is $= \frac{5 !}{3 ! 2 !} \times 2 \times 2 = 40$