<p>The sum of all four-digit numbers that can be formed by using the digits 2, 4, 6, 8 (when repetition of digits is not allowed) is</p>
Step-by-Step Solution
Key Concept: Each digit appears in each position (units, tens, hundreds, thousands) equally often due to symmetry. Calculate frequency per position, then use place value to find total sum.
<p><strong>Step 1:</strong> Total four-digit numbers using 2, 4, 6, 8 without repetition = 4! = 24</p><p><strong>Step 2:</strong> By symmetry, each digit appears in each position (units, tens, hundreds, thousands) equally often.</p><p>Frequency of each digit in each position = 24 ÷ 4 = 6 times</p><p><strong>Step 3:</strong> Sum of digits = 2 + 4 + 6 + 8 = 20</p><p><strong>Step 4:</strong> In units place: each digit appears 6 times<br>Contribution = 6 × 20 × 1 = 120</p><p><strong>Step 5:</strong> In tens place: each digit appears 6 times<br>Contribution = 6 × 20 × 10 = 1200</p><p><strong>Step 6:</strong> In hundreds place: each digit appears 6 times<br>Contribution = 6 × 20 × 100 = 12000</p><p><strong>Step 7:</strong> In thousands place: each digit appears 6 times<br>Contribution = 6 × 20 × 1000 = 120000</p><p><strong>Step 8:</strong> Total sum = 120 + 1200 + 12000 + 120000 = 133320</p><p>∴ Answer: B</p>
Correct Answer: B