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InterviewSolution
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How many different seven digit numbers are there the sum of whose digits is even ? |
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Answer» Let us consider 10 successive 7-digit numbers. `a_(1)a_(2)a_(3)a_(4)a_(5)a_(6)" "0,` `a_(1)a_(2)a_(3)a_(4)a_(5)a_(6)" "1`, `a_(1)a_(2)a_(3)a_(4)a_(5)a_(6)" "2`, . . . . . . . . . `a_(1)a_(2)a_(3)a_(4)a_(5)a_(6)" "9`, where `a_(1),a_(2),a_(3),a_(4),a_(5) and a_(6)` are some digits, we see that half of these 10 numbers, i.e., 5 numbers have an even sum of digits. the first digit `a_(1)` can assume 9 different values and each of the digits `a_(2),a_(3),a_(4),a_(5) and a_(6)` can assume 10 different values. the last digit `a_(7)` can assume only 5 different values of which the sum of all digits is even. `therefore` There are `9xx10^(5)xx5=45xx10^(5)`, 7-digit numbers the sum of whose digits is even. |
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