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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

0001000111 Fri, Jun 18, 2021 6:05 AM

> If I choose 6 objects what’s the prob that I choose at least one object from each of the three groups.

0001000111 Fri, Jun 18, 2021 6:05 AM

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