We have y urns of balls. In each urn, we have x balls in the same color. But balls in different urns have difference color.
Now, without replacement, we draw y balls randomly. What is the chance that we drawn from z different urns or more?
We have y urns of balls. In each urn, we have x balls in the same color. But balls in different urns have difference color.
Now, without replacement, we draw y balls randomly. What is the chance that we drawn from z different urns or more?
Let's see. I'll assume there are enough balls in each urn that it can be picked from indefinitely. (that is to say each urn would have y balls)
If y = 1, then the chance is 0% (trivial, since you can't choose a different urn if you only have one)
If y = 2, then the possibilities are (let numbers be the colors)
1 1
1 2
2 1
2 2
so the probability is 1/2
If y = 3, then there are 27 possibilities. I counted 18 that weren't all a single color are possible, so the probability would be 2/3.
At this point, I smell an induction proof, and I'm sure there's an easier way with permutations and combinations.
We have y urns of balls. In each urn, we have x balls in the same color. But balls in different urns have difference colors.
Now, without replacement, we draw y balls randomly. What is the chance that we get z(z>=2) different colors or more?