SOLUTION: Find the sum of all four digit numbers that can be formed using the digits 0,1,2,3,4, each digit appearing at most once

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Question 917724: Find the sum of all four digit numbers that can be formed using the digits 0,1,2,3,4, each digit appearing at most once
Answer by KMST(5328) About Me  (Show Source):
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There are 5 possible choices for the each of the last 3 digits.
The first digit cannot be 0, so there are only 4 choices for the first digit.
That gives us a total of 4%2A5%2A5%2A5=500 numbers.

The average of the unit digits is %280%2B1%2B2%2B3%2B4%29%2F5=10%2F5=2 .
So the sum of all the unit digits is 500%2A2=1000
The same goes for the tens digits and the hundreds digits,
so the sum of all tens digits is 1000, for a sum value of 10,000,
and the sum of all hundreds digits is 1000, for a sum value of 100,000
The average of the first digits is %281%2B2%2B3%2B4%29%2F4=10%2F4=2.5 .
So the sum of all the first digits in all those 500 numbers must be
500%2A2.5=1250 .
The value of that sum is (1000)(1250)=1,250,000.
The value of the sum of all 500 numbers is
1,250,000+100,000+10,000+1000=1,361,000.