An examination paper consists of two sections. Section I contains 5 Algebra and 4 Calculus questions, while Section II contains 4 Algebra and 5 Calculus questions. A student is required to answer exactly 4 Algebra and 4 Calculus questions in total. If the student must attempt exactly 5 questions from Section I and 3 questions from Section II, the total number of ways the student can choose the questions is :

Step-by-step solution

Let the number of Algebra and Calculus questions chosen from Section I be a and c respectively. Then the number of Algebra and Calculus questions chosen from Section II must be 4-a and 4-c respectively. Since the student must attempt 5 questions from Section I, a + c = 5 . The possible cases for (a, c) are (4, 1), (3, 2), (2, 3), and (1, 4) . Case 1: 4 Algebra and 1 Calculus from Section I, and 0 Algebra and 3 Calculus from Section II. Number of ways = (⁵C₄ ⁴C₁) (⁴C₀ ⁵C₃) = (5 4) (1 10) = 200 . Case 2: 3 Algebra an