Let's consider a system that requires 9 character long password. and there are 0~9, a-z, A-Z and at least 2 different categories in the 9 characters' password.
I saw other questions with "at least one different letter" but since this requires at least 2 different categories
How can I find the combination of the passwords?
On
Your question is worded oddly, so I'll reword it to make sure we're on the same page. I believe you're asking: "How many unique 9 character passwords exist are comprised exclusively of at least two of the following categories of characters: capital letters, lowercase letters, and numbers?". Assuming this is your question, the way I would go about solving this is by finding the total number of 9 character alphanumeric passwords, $(26+26+10)^9=62^9\simeq1.354\times10^{16}$, then subtracting the number of 9 character passwords that use only one of the categories, $26^9+26^9+10^9\simeq1.086\times10^{13}$. This brings us to a value of roughly $1.353\times10^{16}$.
The total number of possible passwords is $(10 + 26 + 26)^9 = 62^9$
This number includes all the passwords with $1$, $2$ and $3$ categories. So, from this, we subtract the count of passwords with only one category of letters.
For $0-9$ category, we subtract $10^9$.
For $a-z$ category, we subtract $26^9$.
For $A-Z$ category, we subtract $26^9$.
Total: $\boxed{62^9 - 10^9 - 2 \cdot 26^9}$