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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?

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There will be as many ways as there are ways of filling 3 vacant places  in succession by the given six digits. In this case, the units place can be filled by 2 or 4 or 6 only i.e., the unit place can be filled by 3 ways. The tens place can be filled by any of the 6 digits in 6 different ways and also the hundreds place can be filled by any of the 6 digits in 6 different ways, as the digits can be repeated.
Therefore, by multiplication principle, the required number of three digit even numbers is 3 x 6 x 6 = 108

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