My combinatorics are very rusty and I hope you guys can help me with this kind of question. Lets say there is a bag with 50 balls in it. There are 5 black balls and 45 white balls. How to calculate the probability of picking exactly 2 black balls given 4 picks. How would this differ if we would need to get at least 2 black balls out of 4 picks?
EDIT : all 4 balls are picked at once
$\frac{{5\choose 2}\cdot {45\choose 2}}{50\choose 4}$ for part $1$.
For part $2$, there are $\frac{{5\choose 2}\cdot{45\choose 2}+{5\choose 3}\cdot{45\choose1}+{5\choose 4}}{50\choose 4}$.