<p>The sum of the digits in the unit's place of all the 4-digit numbers formed by using the numbers 3, 4, 5 and 6, without repetition, is</p>
Step-by-Step Solution
Key Concept: Each of the 4 digits appears in the unit's place equally often. Since there are 4! = 24 total 4-digit numbers and 4 choices for unit's place, each digit appears in unit's place exactly 24/4 = 6 times.
<p><strong>Step 1:</strong> Find total 4-digit numbers formed using 3, 4, 5, 6 without repetition.</p><p>Total numbers = 4! = 24</p><p><strong>Step 2:</strong> Determine how many times each digit appears in the unit's place.</p><p>By symmetry, each of the 4 digits appears in each position (unit's, ten's, hundred's, thousand's) equally often.</p><p>Number of times each digit appears in unit's place = 24/4 = 6</p><p><strong>Step 3:</strong> Calculate sum of digits in unit's place.</p><p>Each digit {3, 4, 5, 6} appears 6 times in the unit's place.</p><p>Sum = 6(3 + 4 + 5 + 6) = 6(18) = 108</p><p>∴ Answer: B</p>
Correct Answer: B