Counting: Videos & Practice Problems

A security system uses a $6$-digit passcode with the following rules:

• The first digit must be between $3$ and $7$ (inclusive).
• The next two digits can be any number from $0$ to $9$.
• The last three digits can also be any number from $0$ to $9$, except that all three digits cannot be the same (to avoid passcodes like $111$, $222$, etc.).

(i) How many different $6$-digit passcodes are possible under these rules?
(ii) Given that the system is used by $50$ million devices, are there enough available passcodes?