An examination contains 3 sections, each having 6 questions. In how many ways a student can attempt 12 questions such that in each section he has to attempt at least 3 questions and at the most 5 questions?

We need to choose 12 questions from 18 (3 sections of 6). Constraints: 3 <= n_i <= 5 for each section i, and sum(n_i) = 12. Possible distributions (n1, n2, n3): (4,4,4), (3,4,5) in 6 permutations, (3,3,6) is invalid. Calculating combinations: C(6,4)^3 + 6 * C(6,3)*C(6,4)*C(6,5) = 15^3 + 6 * (20 * 15 * 6) = 3375 + 10800 = 14175.