The number of ways in which an examiner can assign 30 marks to 8 questions, giving not less than 2 marks to any question, is :

Step-by-step solution

30 marks to be alloted to 8 questions. Each question has to be given 2 marks Let questions be a, b, c, d, e, f, g, h and a+b+c+d+e+f+g+h=30 Let a=a₁+2 so, a₁ 0b=a₂+2 so, a₂ 0, . a₈ 0 So, . array c a₁+a₂+ +a₈ +2+2+ . .+2 array =30 a₁+a₂+ +a₈=30-16=14 So, this is a problem of distributing 14 articles in 8 groups. Number of ways = ¹⁴⁺⁸⁻¹ C _ 8-1 = ²¹ C ₇