# Probability of getting k different colored balls from an urn with K different colors of balls, each color has the same number of balls

Let's say I have an urn with $$n$$ balls, with $$K$$ different colors of balls, where each color has the same number of balls: $$\frac{n}{K}$$. Given I reach into the urn and grab a ball (without replacement) $$m$$ times, what is the probability of getting $$k$$ different colors of balls?

I asked the same question here, and has one person commenting on it. I am wondering if anyone on this forum has additional useful insight.

• You really need to show what you have tried. For example, what is the probability the first ball drawn is a new colour? (hint: $1$) If it is, then what is the probability the second draw is a new colour and what is the probability the two draws are different. And so on. Commented Jul 22, 2022 at 21:10
• You want multivariate hypergeometric distribution en.wikipedia.org/wiki/…
– Tim
Commented Jul 22, 2022 at 21:38
• @Tim: do you want to turn that into an answer? Commented Jul 23, 2022 at 7:15