A bag contains 100 red balls, 10 green balls, and some blue balls.

How many blue balls would maximize the probability that you could pick 3 balls without replacement and they would all end up being different colors (i.e. one red, one blue, and one green)?

If there are multiple answers, please provide the answer as the sum of all such answers. That is, if \(a\) and \(b\) both maximize the probability, the answer would be \(a+b\).

Assume that there are no other colors in the bag.

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