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How many 3-digit even numbers can be formed from the digits 1,2,3,4,5,6 if the digits can be repeated?

$\begin{array}{1 1}(A)\;100\\(B)\;104\\(C)\;108\\(D)\;110\end{array} $

1 Answer

Let 2 be fixed at unit's place.The ten's place can be filled up in 6 ways.The hundred is place can be also be filled in 6 ways.
No of numbers that can be formed when 2 is at unit's place=$6\times 6=36$
Similarly when 4 is at unit's place,the number of numbers that can be formed =36
Again when 6 is at the unit's place.The number of numbers that can be formed =36
$\therefore$ The total numbers of ways when 3 digits numbers can be formed,the digits being repeated =$36\times 3=108$
Hence (C) is the correct answer.
answered May 13, 2014 by sreemathi.v

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