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In the decimal system of numeration the number of 6-digit numbers in which the sum of the digits is divisible by 5 is

$\begin{array}{1 1}(A)\;180000\\(B)\;540000\\(C)\;5\times 10^5\\(D)\;\text{None of these}\end{array} $

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Ways : 9 10 10 10 10 2
0 cannot be placed in the first place.In the other four places any digit can go.After filling the first five places,the last place can be filled by 0 or 5
$\therefore$ The required number of numbers =$9\times 10^4\times 2$
$\Rightarrow 18\times 10^4$
$\Rightarrow 180000$
Hence (A) is the correct answer.
answered May 20, 2014 by sreemathi.v

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