OK the problem came from an AI course that I attended this year. You can find the problem description here
In short we have a number of birds in the sky that we need to shoot down.
In the main problem there are 90 white birds, 23 yellow, 22 blue, 22 green, 22 red and 1 black for a total of 180 birds.
My question is: How can I find the probability that I will have killed at least one of each species after X kills?
I know it is somehow connected to the hypergeometric distribution because that can tell you what is, for example, the probability that you will have hit the black bird after X number of kills, since we can treat each kill as sampling without replacement. But how do I do this for all the species?
I'm asking this because one of my strategies required at least one killed bird from each species to use as example data, and I'm not sure how I could get a number that would say:
"After X kills you have P probability that you have hit at least one bird from each species".