Problem source

I know that 
ice-creams come in $n$ different sizes, but I don't know what the sizes are.
I am offered one of each in 
succession, in random order.
I am certainly going to choose one - the bigger
the better -  but I
am not allowed more than one. My strategy is to reject the first  
ice-cream I am offered
 and choose the  first one thereafter  that is bigger than the first 
one I was offered; if the first ice-cream offered is in fact the biggest one,
then I have to put up with the last one, however small.
Let $\P_n(k)$ be the probability that I choose the $k$th biggest ice-cream,
where $k=1$ is the biggest and $k=n$ is the smallest.
\begin{questionparts}
\item Show that $\P_4(1) = \frac{11}{24}$ and find $\P_4(2)$, $\P_4(3)$
and $\P_4(4)$.
\item Find an expression  for $\P_n(1)$.
\end{questionparts}