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Question
How many 3-digit even numbers can be formed from the digits 1, 2, 3, 4, 5, 6 if the digits can be repeated?
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Solution
There will be as many ways as there are ways of filling 3 vacant places 
in succession with the given six digits. In this case, the units place can be filled by 2 or 4 or 6 only, i.e., the units place can be filled in 3 ways. The tens place can be filled by any of the 6 digits in 6 different ways and the hundreds place can be filled by any of the 6 digits in 6 different ways, as the digits can be repeated.
Therefore, by the multiplication principle, the required number of three digit even numbers is 3 × 6 × 6 = 108.
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