<p>The number less than 1000 that can be formed using the digits 0, 1, 2, 3, 4, 5 when repetition is not allowed is equal to</p>
Step-by-Step Solution
Key Concept: Numbers less than 1000 include 1-digit, 2-digit, and 3-digit numbers. For each category, treat 0 specially since it cannot be a leading digit, then count arrangements systematically.
<p><strong>Step 1: One-digit numbers (1-9)</strong></p><p>We can use digits: 1, 2, 3, 4, 5 (cannot use 0)</p><p>Count = 5</p><p><strong>Step 2: Two-digit numbers (10-99)</strong></p><p>First digit: Choose from {1, 2, 3, 4, 5} = 5 choices</p><p>Second digit: Choose from remaining 5 digits (including 0) = 5 choices</p><p>Count = 5 × 5 = 25</p><p><strong>Step 3: Three-digit numbers (100-999)</strong></p><p>First digit: Choose from {1, 2, 3, 4, 5} = 5 choices</p><p>Second digit: Choose from remaining 5 digits (including 0) = 5 choices</p><p>Third digit: Choose from remaining 4 digits = 4 choices</p><p>Count = 5 × 5 × 4 = 100</p><p><strong>Step 4: Total</strong></p><p>Total numbers = 5 + 25 + 100 = <strong>130</strong></p><p>∴ Answer: D</p>
Correct Answer: D