green and y black balls, whats the probability if we take 6 that 2

will be black etc. are easily solvable with hypergeometric and binomial distribution. Is there a distribution that solves it a general case for example:

Given 1000

blue, 1200 green, 2000 red balls we draw 20 balls.

Let x be the number of drawn blue balls currently, y-green, z-red(all currently drawn). If at any draw this condition is satisfied: y^3-z^2>x^2.5 . We add ONCE to the urn this configuration and continue the drawing

we add to the urn:

- The number of green balls drawn as green
- Twice the number of red balls as red
- Cubed the numbers of blue balls as blue.

Is this solvable?