A student is to answer 10 out of 13 questions in an examination such that he must choose at least 4 from the first five questions. The number of choices available to him is
- A. 140
- B. 196
- C. 280
- D. 346
Answer: B. 196
Explanation: Number of questions to choose = 10 out of 13 with at least 4 from first 5: Case 1: 4 from first 5 and 6 from remaining 8: C(5,4) × C(8,6) = 5 × 28 = 140. Case 2: 5 from first 5 and 5 from remaining 8: C(5,5) × C(8,5) = 1 × 56 = 56. Total choices = 140 + 56 = 196.