In a certain factory, each worker is given a security code, which must meet two criteria.
(1) It contains at least one even and at least one odd digit
(2) It contains at least three different digits
1. Let's first find the total number of combinations with five digits: $10^5$ (zero is valid at the beginning of the code)
2. Let's find the number of combinations which do not meet the first criterion: $5^5 + 5^5 = 2*5^5$
3. Now, let's find the number or combinations which do not meet the second criterion: It contains one number that is even and one that is odd $10\cdot5$ and excludes the numbers that have only odd and even digits ($2^5-2)$ So, the number we are looking for is: $(2^5-2)(10)(5)$
4. We sum everything up and get the answer: $10^5-2*5^5-50*(2^5-2)$
Could you please review my attempt to solve this problem?