Question 285734: find the sum of all the four digit number that can be obtained by using the digits 1,2,3,4 once in each.
Answer by Edwin McCravy(20060)   (Show Source):
You can put this solution on YOUR website!
There are 4! or 24 such numbers. So there are 24 digits in each column.
There are the same number of 1's in each column as there are 2's, 3's
and 4's. so there are 24÷4 or 6 of each digit in each column. So each
column sums to 6*1+6*2+6*3+6*4 = 6(1+2+3+4) = 6(10) = 60, so the sum is
the sum of the thousands column, which is 60, times 1000 plus
the sum of the hundreds column, which is 60, times 100 plus
the sum of the tens column, which is 60, times 10 plus
the sum of the units column, which is 60.
1000(60) + 100(60) + 10(60) + 60 = 60(1000+100+10+1) = 60(1111)= 66660
And since there are only 24 of them, you can check just by adding;
1234
1243
1324
1342
1423
1432
2134
2143
2314
2341
2413
2431
3124
3142
3214
3241
3412
3421
4123
4132
4213
4231
4312
+4321
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66660
Edwin
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