"You've been hired as a security consultant. The vault's owner wants to know exactly how many codes their system allows — get the count wrong, and you'll either miss a real vulnerability or waste money fixing one that isn't there."
4-character code, digits 0–9, repeats allowed. How many codes?
Now try 6 characters. Can you write a general rule for length \(n\)?
Same code, but no digit may repeat. How many now?
Why isn't this just "a bit less than before"?
Add: the code can't start with 0. Does the answer change?
36-character alphabet (digits + letters), repeats allowed, must contain at least one letter. How many codes?
If that got messy, is there a completely different approach?
Combine every rule: 36 characters, no repeats, at least one letter. Explain how you used ideas from both Phase 2 and Phase 3.
Add: the first character must specifically be a letter. Does the "at least one letter" rule still need separate handling?