SOLUTION: If 4 factories in a group of 20 factories in a community are violatig environmental regulations and 6 are randomly selected for inspection, what is the probability that none of the

Question 344440: If 4 factories in a group of 20 factories in a community are violatig environmental regulations and 6 are randomly selected for inspection, what is the probability that none of the violators will be selected?
What formula do I even begin to solve this problem with?
Found 2 solutions by stanbon, jrfrunner:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
If 4 factories in a group of 20 factories in a community are violatig environmental regulations and 6 are randomly selected for inspection, what is the probability that none of the violators will be selected?
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The probability a randomly selected factory is not
a violator is 16/20 = 4/5
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The probability 6 of 6 are not violators is (4/5)^6 = 0.2621
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Cheers,
Stan H.
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Answer by jrfrunner(365) (Show Source): You can put this solution on YOUR website!
let N=event the chosen factory is a non violator
each outcomes probability is dependent on what was selected previously
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P(selecting 6 at random and getting none of the violators)=P(NNNNNN)
= (16/20)*(15/19)*(14/18)*(13/17)*(12/16)*(11/15) = 0.2066
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this probability could also be written as
C(4,0)*C(16,6)/C(20,6) basically # ways choosing 0 of the 4 violators times # ways of choosing 6 nonviolators out of 16 nonviolators divided by the # ways of selecting 6 factories out of 20

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