Question 1070031: find the sum of all 5 digit numbers that can be formed by using the digits 2,3,5,7 and 8, where each of these digits appears in each number.
Answer by Edwin McCravy(20056) (Show Source):
You can put this solution on YOUR website!
Suppose you had them all lined up in a column to add:
23578
23587
23758
23785
23857
23875
25378
...
85732
87235
87253
87325
87352
87523
+87532
=======
There are 5!=120 numbers to be added. One 5th of
the numbers in each column are 2's, one-fifth are 3's,
and so on to one-fifth are 8's, So since one-fifth of
120 is 24, the sum of each column is
24*(2+3+5+7+8) = 24*(25) = 600
So there are
600 ten-thousands +
600 thousands +
600 hundreds +
600 tens +
600 ones
or
6000000 +
600000 +
60000 +
6000 +
600
========
6666600
Edwin
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