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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?


Solution

A three digit even number is to be formed from given $$6$$ digits $$1,2,3,4,5,6$$.
$$\Box \Box \Box \\ H T O$$

Since, for the number is to be even , so ones place can be filled by $$ 2, 4$$ or $$6$$. So, there are $$3$$ ways to fill ones place.

Since, repetition is allowed , so tens place can also be filled by $$6$$ ways.
Similarly,hundreds place can also be filled by $$6$$ ways.
So, number of ways in which three digit even numbers can be formed from the given digits is $$6\times 6\times 3=108$$

Mathematics
NCERT
Standard XI

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