how many 9 digit numbers have the property that the product of their firsts and last digits is even? How many 9 digit numbers have the property that the product of their firsts and last digits is even?
I tried listing them out, but there's probably way too many. This is a basic counting problem.

The product of the first and last digits is even iff they are not both odd. There are $9×10$ ways to choose the first and last digits; of those $5×5$ result in an odd product due to both digits being odd. The remaining seven digits may be chosen arbitrarily, so the answer is $(9×10-5×5)10^7=65\cdot10^7$.
