In an examination of Mathematics paper, there are 20 questions of equal marks and the question paper is divided into three sections : A , B and C . A student is required to attempt total 15 questions taking at least 4 questions from each section. If section A has 8 questions, section B has 6 questions and section C has 6 questions, then the total number of ways a student can select 15 questions is _________.

Step-by-step solution

Given, Mathematics paper has 20 questions of equal marks and have three sections A , B & C , also A has 8 questions, B has 6 questions and C has 6 questions, Now, if 4 questions from each section are selected, then remaining 3 questions can be selected either in ( 1 , 1 , 1 ) or ( 3 , 0 , 0 ) or ( 2 , 1 , 0 ) as we have already selected 4 × 3 = 12 questions So, the total ways will be = C 5 8 · C 5 6 · C 5 6 + C 6 8 C 5 6 · C 4 6 × 2 + C 5 8 · C 6 6 · C 4 6 × 2 + C 4 8 · C 6 6 · C 5 6 × 2 + C 7 8 · C 4 6 · C 4 6 = 5