Imagine a bag has some balls, some blue some red. Lets say there are 50 balls. 5 are red and 45 are blue. I have 4 bins, and am going to randomly pick balls out of the bag and put them into the bins until i have filled each bin with 5 balls. I want to know the probability that exactly 3 out of the 4 bins have at least one red ball, and the other bin has all blue balls. How can I find this probability?
I thought about using a binomial distribution, where the probability of success is the probability of a bin having at least one red. However, this probability will not be constant over the different trials as there is no ball replacement. Once a ball is taken out of the bag to fill a bin, it is not put back.