Combinatorics

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Combinatorics

If I have x groups of equal sizes taken from a population of size n = 3x (I have 3 groups) what is the probability that I choose at least one object from each group if I am choosing 6 objects? The objects are selected uniformly at random from population. I know that there are 5 choose 2 ways of choosing integers for x_1+x_2+x_3=6 but don’t think that’s part of the answer.

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I meant I have 3 groups of size x, let x be 30 and n be 90
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If I choose 6 objects what’s the prob that I choose at least one object from each of the three groups.
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