Discussion
The sum of all 3-digit numbers that can be formed using 1, 2, 3, 4 without repetitions is
Answer: E
The sum is 6660.
The number of 3-digit numbers with distinct digits from 1, 2, 3, 4 is \({}^{4}P_{3} = 24\). By symmetry each digit appears in each place (hundreds, tens, units) \(24 \div 4 = 6\) times.
\[ \begin{aligned} \text{sum of each place} &= 6(1 + 2 + 3 + 4) = 60 \\ \text{total} &= 60 \times (100 + 10 + 1) = 6660 \end{aligned} \]
The other options are not multiples of 111, which every such total must be, so they can be rejected without further work.
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