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A bag consists of three differently colored bottles, which includes 3

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micv
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A bag consists of three differently colored bottles, which includes 3 [#permalink] New post   30 Apr 2020, 15:11
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A bag consists of three differently colored bottles, which includes 3 black, 4 white, and 5 red. If 3 bottles are picked randomly from the bag, what is the probability that all the bottles selected are not white?

A) 8C3/12C3
B) 1 - (4C3/12C3)
C) 1 - (4C3/8C3)
D) 3C3/12C3
E) 1 - (8C3/12C3)

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Re: A bag consists of three differently colored bottles, which includes 3 [#permalink] New post   30 Apr 2020, 17:12
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Poorly worded question IMO

"All the bottles selected are not white" is different from "Not all the bottles selected are white"

"All the bottles selected are not white" means that we cannot have even one white bottle among our picks. So this can be BBB, RRR, BBR, BRB, RBB, RRB, RBR, BRR. In this case the probability will be 8C3/12C3

"Not all the bottles selected are white" means we can have white bottles among our picks as long as we don't get 3 white bottles. In this case the answer would be 1-(4C3/12C3)

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Re: A bag consists of three differently colored bottles, which includes 3 [#permalink] New post   30 Apr 2020, 17:46
Think you mixed up the solution. Thanks anyway.
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Re: A bag consists of three differently colored bottles, which includes 3 [#permalink] New post   01 May 2020, 11:27
micv wrote:
A bag consists of three differently colored bottles, which includes 3 black, 4 white, and 5 red. If 3 bottles are picked randomly from the bag, what is the probability that all the bottles selected are not white?

A) 8C3/12C3
B) 1 - (4C3/12C3)
C) 1 - (4C3/8C3)
D) 3C3/12C3
E) 1 - (8C3/12C3)


Total no of ways to choose any 3 bottles from the total 12 bottles = 12C3
Total no of ways to choose only black and red bottles = 8C3
Probability = 8C3/12C3
A is the answer
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Re: A bag consists of three differently colored bottles, which includes 3 [#permalink] New post   01 May 2020, 12:24
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As firas points out, there's no way to even tell what the question means, because it's open to two different interpretations (it's barely written in English). And just as problematic are the answer choices. You will absolutely never see the notation "8C3" on the GMAT. You don't even see that notation in real mathematics; it's just a convenience for internet forums since the standard mathematical notations are hard to type. You can see factorial notation in GMAT answer choices, but never the specialized notations for permutations or combinations. It's better to work from sources that more closely resemble the real test.

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Re: A bag consists of three differently colored bottles, which includes 3 [#permalink]
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