Problem source

I have $k$ different keys on my key ring. When I 
come home at night I try one key after another until I 
find the key that fits my front door. What is the probability 
that I find the correct key in exactly $n$ attempts in 
each of the following three cases?
 \begin{questionparts}
 \item At each attempt,
I choose a key that I have not tried 
before but otherwise each choice is equally likely. 
 
\item At each attempt,
I choose a key from all my 
keys and each of the $k$ choices is equally likely. 
 
\item
At the first attempt,
I choose from all my 
keys and each of the $k$ choices is equally likely. Thereafter, 
I choose from the keys that I did not try the previous time 
but otherwise each choice is equally likely. 
 \end{questionparts}