<p>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</p>
Step-by-Step Solution
Key Concept: Break the problem into mutually exclusive cases based on the constraint 'at least 4 from first 5 questions', then count selections from remaining questions accordingly.
<p><strong>Step 1:</strong> Identify constraint: Choose at least 4 from first 5 questions, and total 10 questions overall.</p><p><strong>Step 2:</strong> Set up cases based on selections from first 5 questions:</p><p><strong>Case 1:</strong> Choose exactly 4 from first 5 questions</p><p>Selections from first 5: C(5,4) = 5</p><p>Remaining to choose: 10 - 4 = 6 from last 8 questions: C(8,6) = 28</p><p>Subtotal: 5 × 28 = 140</p><p><strong>Case 2:</strong> Choose exactly 5 from first 5 questions</p><p>Selections from first 5: C(5,5) = 1</p><p>Remaining to choose: 10 - 5 = 5 from last 8 questions: C(8,5) = 56</p><p>Subtotal: 1 × 56 = 56</p><p><strong>Step 3:</strong> Add both cases (mutually exclusive events):</p><p>Total = 140 + 56 = 196</p><p>∴ Answer: B</p>
Correct Answer: B