So there are $10$ combinations for each digit except the last which has 5 possibilities ($0,2,4,6,8$). Thus $10*10*10*10*10*10*10*5=50000000$ combinations right?
As a follow up, how many strings of 8 digits have at least one repeated digit?
I'm not sure how to approach this one. The first digit you have $10$ possibilities and then the next digit you only have $1$ possibility and for the next $6$ digits you have $10$ possibilities for each.