(a) $n$ identical chocolates are to be distributed among the $k$ students in Tinku's class. Find the probability that Tinku gets at least one chocolate, assuming that the $n$ chocolates are handed out one by one in $n$ independent steps. At each step, one chocolate is given to a randomly chosen student, with each student having equal chance to receive it.
(b) Solve the same problem assuming instead that all distributions are equally likely. You are given that the number of such distributions is $\binom { n + k - 1 } { k - 1 }$. (Here all chocolates are considered interchangeable but students are considered different.)