Here’s a few similar puzzles with a common story:

I have n safes, each one with a unique key that opens it. Unfortunately, some prankster snuck into my office last night and stole my key ring. It seems they’ve randomly put the keys inside the safes (one key per safe), and locked them.

We’ll play around with a few different conditions and see what chances we have of getting all safes unlocked, and at what cost.