Question: By using the digits 1, 2, 3, 4 and 5, 5-digit numbers are formed such that every digit is used at most once, then find the sum of all such possible numbers.
Attempt: I found the answer 3,999,960. The sum of digits at unit place will be
$$s = 24 * ( 5+4+3+2+1) $$
Now adding s for every place - unit, tenth, hundredth, thousandth, and ten-thousandth.
But there must some other ways also to approach this problem. I would like to understand about them. Thanks.