 Hi and how are you all today? Let us discuss this question. It says how many three-digit even numbers can be formed from the digits 1, 2, 3, 4, 5, 6 if the digits can be repeated. So here what we need to take care first of all, we need to make a three-digit even number and the digits can be repeated. Right? So here we will be using the fundamental principle of counting or multiplication principle in order to find out our answer. Now let us start with our solution. There are many numbers as there are ways of filling digits in the three vacant places. Right? Now let these be three vacant places. What we need to do here is we need to fill in the six given digits and they are 1, 2, 3, 4, 5 and 6. One thing which we need to note is that here we are making an even digit. We need to make an even digit. So we have to count only even numbers to fill up the unit place. So the unit place can be filled up with only 2, 4 and 6. So that means the unit place can be filled in three different ways. The tense place now can be filled up with any of the six digits as the repetition is allowed. So there are six different ways of filling up the digit that will be on this tenth place. The unit digit can be filled up in three different ways. The tense place can be filled up in six different places. Now the remaining one is 100 place digit. It can also be filled up by any of the six digits that are given to us and hence there are six different ways of filling this place also. Thus the number of ways in which these three vacant places can be filled in by the principle of multiplication will be 3 multiplied by 6 multiplied by 6. That is equal to 108. So our final answer is what it is 108. So with the help of the multiplication principle or the fundamental principle of counting we were able to solve this question. Take care.