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?

Answer 1

A three digit even number is to be formed from given $6$ digits $1,2,3,4,5,6$.
$\square \square \square HTO$

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 $6\times 6\times 3=108$