125. Formation of integers. Can the reader name the sum of all integers formed from the four digits $1,2,3,4$? In other words, it is required to calculate the sum of such numbers as $1234,1423,4312$, etc. Of course, one could write down all such numbers in a row and then add them up. However, it is more interesting to find a simple rule that can be used to find the sums of numbers formed from four different arbitrarily chosen (non-zero) digits.
125. If you multiply 6666 by the sum of four given digits, you will get the correct answer. Since \(1,2,3,4\) add up to 10, 
multiplying 6666 by 10 gives us the answer 66660. If we seek the sum of all combinations of four different digits, we get 16798320, or \(6666 \times 2520\).