How many $2$ digit even numbers can be formed from the digits $1, 2, 3, 4, 5$ if the digits can be repeated?

Step 1: Identify the constraints

We need to form a 2-digit even number using the digits 1, 2, 3, 4, 5. The digits can be repeated. A 2-digit number has a tens place and a units place.

Step 2: Determine options for the units place

For a number to be even, its units digit must be an even number. From the given digits {1, 2, 3, 4, 5}, the even digits are 2 and 4. So, there are 2 choices for the units place.

Step 3: Determine options for the tens place

Since the digits can be repeated, the tens place can be any of the five given digits {1, 2, 3, 4, 5}. So, there are 5 choices for the tens place.

Step 4: Calculate the total number of even numbers

To find the total number of 2-digit even numbers, we multiply the number of choices for the tens place by the number of choices for the units place. This gives us $5 \times 2 = 10$ possible numbers.

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