The question is just for fun, and I feel like I'm missing a clever way of thinking about it.
suppose that you are on an alien planet, and you are trying to learn their language. You break into one of the aliens houses and get on his computer and print the contents of a file by accident. you have to figure out if this document is written in their language, or if it's just a binary file.
the idea here I think is that the alphabet for the language is smaller than the alphabet for a printed binary file. You would expect many more repeats from the string with the smaller language. after some string length, you would be able to give a pretty good estimate of the number of letters in the alphabet from which the text was written.
anyway, the question is, what is the probability of a string of length $n$ chosen randomly with an alphabet of size $m$ will have $k$ unique letters?