We will see that there are 50,000 different possible codes that start with an even number.

How many possible codes are there?

We know that the code has 5 digits, each one with 10 possible options (except the first one, when we only can use even digits, so there we have 5 options).

And the numbers can be repeated any number of times through the code, then the total number of different codes that can be made is equal to the product between the numbers of options for each of the digits, we will have:

[tex]C = 5*10*10*10*10 = 50,000[/tex]

So there are 50,000 different codes.

If you want to know more about combinations: