Question:

<p><strong>Step 1:</strong> Find sum of ALL 3-digit numbers (100-999).</p><p>Count = 900 numbers. Using the formula for arithmetic series or digit contribution:</p><p>Sum of all 3-digit numbers = 900 × (100+999)/2 = 900 × 549.5 = 494,550</p><p><strong>Step 2:</strong> Find sum of 3-digit numbers with ALL ODD digits.</p><p>Odd digits: {1,3,5,7,9} (5 choices each position). Count = 5³ = 125.</p><p>Hundreds place contribution: (1+3+5+7+9) × 25 × 100 = 25 × 25 × 100 = 62,500</p><p>Tens place contribution: (1+3+5+7+9) × 25 × 10 = 25 × 25 × 10 = 6,250</p><p>Units place contribution: (1+3+5+7+9) × 25 × 1 = 25 × 25 = 625</p><p>Sum (all odd) = 62,500 + 6,250 + 625 = 69,375</p><p><strong>Step 3:</strong> Find sum of 3-digit numbers with ALL EVEN digits.</p><p>Even digits for hundreds: {2,4,6,8} (4 choices). Even digits for tens/units: {0,2,4,6,8} (5 choices each). Count = 4 × 5 × 5 = 100.</p><p>Hundreds: (2+4+6+8) × 25 × 100 = 20 × 25 × 100 = 50,000</p><p>Tens: (0+2+4+6+8) × 20 × 10 = 20 × 20 × 10 = 4,000</p><p>Units: (0+2+4+6+8) × 20 × 1 = 20 × 20 = 400</p><p>Sum (all even) = 50,000 + 4,000 + 400 = 54,400</p><p><strong>Step 4:</strong> Apply complementary counting.</p><p>k = 494,550 - 69,375 - 54,400 = 370,775</p><p><strong>Step 5:</strong> Calculate k/1000.</p><p>k/1000 = 370,775/1000 = 370.775</p><p>∴ Answer: <strong>370.775</strong> or <strong>370775/1000</strong></p>