<p>How many automobile license plates can be made, if each plate contains two different letters followed by three different digits?</p>
Step-by-Step Solution
Key Concept: Use the fundamental counting principle separately for letters and digits, ensuring 'different' means no repetition allowed within each group.
<p><strong>Step 1: Count arrangements of 2 different letters</strong></p><p>First letter: 26 choices</p><p>Second letter: 25 choices (must be different from first)</p><p>Total letter arrangements = 26 × 25 = 650</p><p><strong>Step 2: Count arrangements of 3 different digits</strong></p><p>First digit: 10 choices (0-9)</p><p>Second digit: 9 choices (must be different from first)</p><p>Third digit: 8 choices (must be different from first two)</p><p>Total digit arrangements = 10 × 9 × 8 = 720</p><p><strong>Step 3: Apply counting principle</strong></p><p>Total plates = (letter arrangements) × (digit arrangements)</p><p>Total plates = 650 × 720 = 468,000</p><p><strong>∴ Answer: 468,000</strong></p>
Correct Answer: 468000