<p>In how many ways can 6 persons stand in a queue?</p>
Step-by-Step Solution
Key Concept: The number of ways to arrange n distinct objects in a line is n!, since each position can be filled by any remaining person and choices decrease sequentially.
<p><strong>Step 1:</strong> Identify that we need to arrange 6 distinct persons in a queue (linear arrangement where order matters).</p><p><strong>Step 2:</strong> For the 1st position: 6 choices</p><p>For the 2nd position: 5 remaining choices</p><p>For the 3rd position: 4 remaining choices</p><p>For the 4th position: 3 remaining choices</p><p>For the 5th position: 2 remaining choices</p><p>For the 6th position: 1 remaining choice</p><p><strong>Step 3:</strong> By the fundamental counting principle, total arrangements = 6 × 5 × 4 × 3 × 2 × 1 = 6! = 720</p><p>∴ Answer: <strong>720</strong></p>
Correct Answer: 720