<p>The number of ways the novels can be arranged is<br/>\(x = {}^6C_4 \times {}^3C_1 \times 4!\)</p><p>What is the value of \(x\)?</p>
Step-by-Step Solution
Key Concept: This is a selection problem disguised as arrangement: first select 4 novels from 6 available (₆C₄), then select 1 shelf from 3 available (₃C₁), then arrange the 4 selected novels on that shelf (4!).
<p><strong>Step 1:</strong> Calculate ₆C₄</p><p>₆C₄ = 6!/(4!×2!) = (6×5)/(2×1) = 15</p><p><strong>Step 2:</strong> Calculate ₃C₁</p><p>₃C₁ = 3</p><p><strong>Step 3:</strong> Calculate 4!</p><p>4! = 24</p><p><strong>Step 4:</strong> Multiply all components</p><p>x = ₆C₄ × ₃C₁ × 4! = 15 × 3 × 24 = 45 × 24 = 1080</p><p>∴ Answer: x = <strong>1080</strong></p>
Correct Answer: D