<p>In how many ways five persons can stand in a row?</p>
Step-by-Step Solution
Key Concept: This is a straightforward linear arrangement problem where all 5 distinct persons must occupy 5 positions in a row. Use the fundamental principle: first position has 5 choices, second has 4 choices, and so on, giving 5!.
<p><strong>Step 1:</strong> Identify that we need to arrange 5 distinct persons in a row (linear arrangement).</p><p><strong>Step 2:</strong> For the first position: 5 choices</p><p>For the second position: 4 choices (one person already placed)</p><p>For the third position: 3 choices</p><p>For the fourth position: 2 choices</p><p>For the fifth position: 1 choice</p><p><strong>Step 3:</strong> By the multiplication principle, total arrangements = 5 × 4 × 3 × 2 × 1 = 5!</p><p><strong>Step 4:</strong> Calculate: 5! = 120</p><p>∴ <strong>Answer: 120</strong></p>
Correct Answer: 120