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_.

 The number of ways a student appearing in the examination gets 5 marks by attepting 5 questions  is_.

  x₁ + x₂ + x₃ + x₄ + x₅ = 5
Only one possibility 3, 3, 3, -2, -2

getting -2 means student may give wrong answers for 2 questions and there are 2 wrong answers for each question(since total number of choices is three)

Number of ways is $=\frac{5!}{3!2!}\times 2\times 2=40$