The Vault Code

The owner tightens the policy: no digit may repeat within a code (still 4 characters, digits 0–9). How many codes are possible now?

In your own words: why isn't this just "a bit less than before"? What's genuinely different about how you have to count each position compared to Phase 1?

The owner adds a further requirement: the code must be a genuine 4-digit number, so it can't start with 0 (repeats still not allowed). Does this change your answer? Work it out.

The owner upgrades the system: each of the 4 characters can now be a digit (0–9) or a letter (A–Z) — 36 possible characters per position, repeats allowed. But there's a new rule: the code must contain at least one letter (an all-digit code is no longer accepted). How many codes satisfy this?

If your method involved separately counting codes with exactly 1 letter, exactly 2, exactly 3, and exactly 4, is there a completely different way to approach this whole problem that avoids all that casework?

The final system: 4 characters from the 36-character alphabet (digits + letters), no repeated characters, and the code must contain at least one letter. How many codes satisfy every rule simultaneously?

Explain how your solution uses ideas from both Phase 2 and Phase 3 — not just one of them.