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Question 394251: Find the sum of all five-digits numbers that are formed by using 1,2,3,4 and 5 once and only once.
Answer by Edwin McCravy(20060)   (Show Source):
You can put this solution on YOUR website!
There are 5! or 120 possible numbers.
if you were to list them all in a column to add, you'd have
12345
12354
12435
12453
13245
.....
.....
.....
54213
54231
54312
54321
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Among all the 120 units digits, 1/5 or 24 of them are 1's,
1/5 or 24 of them are 2's, ... , 1/5 or 24 of them are 5's
24 of them are 1's, so their sum is 24x1 = 24
24 of them are 2's, so their sum is 24x2 = 48
24 of them are 3's, so their sum is 24X3 = 72
24 of them are 4's, so their sum is 24x4 = 96
24 of them are 5's, so their sum is 24x5 = 120
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total of digits in the units column = 360
So the sum of the digits in the units column is 360. The other four
columns also have the same digits as the units digits.
So the sum of each column is 360. So the sum is
360*10000 + 360*1000 + 360*100 + 360*10 + 360
360(10000 + 1000 + 100 + 10 + 1)
360(11111)
3999960
Edwin
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