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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.

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    $\begingroup$ 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. $\endgroup$
    – Henry
    Jul 22, 2022 at 21:10
  • $\begingroup$ You want multivariate hypergeometric distribution en.wikipedia.org/wiki/… $\endgroup$
    – Tim ♦
    Jul 22, 2022 at 21:38
  • $\begingroup$ @Tim: do you want to turn that into an answer? $\endgroup$
    – Stephan Kolassa
    Jul 23, 2022 at 7:15

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