<p>A hall has 12 gates. In how many ways can a man enter the hall through one gate and come out through a different gate?</p>
Step-by-Step Solution
Key Concept: Use the multiplication principle when consecutive operations must be performed in sequence, where the number of ways for the second operation depends on the first being completed.
<p><strong>Step 1:</strong> The man can enter the hall through any of the 12 gates, so there are 12 ways of entering.</p><p><strong>Step 2:</strong> After entering the hall, the man must come out through a different gate. So there are 11 remaining gates to choose from.</p><p><strong>Step 3:</strong> By the Fundamental Principle of Multiplication, the total number of ways = 12 × 11 = 132 ways.</p>
Correct Answer: 132