We have n mailboxes, which each have a key and all keys are distinct. There is a master key which works for every mailbox.
Now, each key is put in one mailbox, and all mailboxes are locked using the master key.
So, what we have here is n locked mailboxes, which each has a key to one of those n mailboxes.
You want to open all the boxes. To start with, you have to break one box, take key from that, and open its corresponding box. When you find key to first box, you have to break another box and so on.
So, given you can break k boxes, what is the probability that you will be able to open all the mailboxes?
Courtesy: Prof. Sharad S. Sane, IIT Bombay.