# Thread: choose y balls, how many distinct colors can you get

1. ## choose y balls, how many distinct colors can you get

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?

2. 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.

3. ## Hi thanks!!

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?