This is an extension of this question: What are Belgium's chances on getting a medal at the 400m finals, given that they have 2 of the 8 athletes?
The original question was: What are the chances of Belgium winning a medal given that they have 2/8 competitors and the probability for a competitor to win is the same for everyone.
The best answer was:
$ \frac{\binom82-\binom52}{\binom82} = \frac9{14} $
My question is, what is the probability to win at least 2 medals given that we have 3/8 competitors?