<p>Numbers greater than 1000 but not greater than 4000 which can be formed with the digits 0, 1, 2, 3, 4 (repetition of digits is allowed) are</p>
Step-by-Step Solution
Key Concept: For numbers between 1000 and 4000, the thousands place can only be 1, 2, or 3 (not 0 or ≥4), while remaining three places can be filled with any of the 5 digits. Multiply the choices for each position.
<p><strong>Step 1:</strong> Identify the range. Numbers must satisfy: 1000 ≤ N ≤ 4000</p><p><strong>Step 2:</strong> Analyze the thousands place. Since we need 4-digit numbers between 1000 and 4000 (inclusive), the thousands digit can be: 1, 2, or 3 only. (Cannot be 0 as it won't form a 4-digit number; cannot be 4 or higher as it exceeds 4000)</p><p><strong>Step 3:</strong> Count choices for thousands place = 3 choices (1, 2, or 3)</p><p><strong>Step 4:</strong> Hundreds place: Can be any digit from {0, 1, 2, 3, 4} = 5 choices</p><p><strong>Step 5:</strong> Tens place: Can be any digit from {0, 1, 2, 3, 4} = 5 choices</p><p><strong>Step 6:</strong> Units place: Can be any digit from {0, 1, 2, 3, 4} = 5 choices</p><p><strong>Step 7:</strong> By fundamental counting principle: Total numbers = 3 × 5 × 5 × 5 = 3 × 125 = <strong>375</strong></p><p>∴ Answer: B</p>
Correct Answer: B