The only items on a shelf are 8 green bins and 4 orange bins. If 3

Question

The only items on a shelf are 8 green bins and 4 orange bins. If 3 bins are to be selected from the shelf, one after the other, at random and without replacement, what is the probability that at least one green bin is selected?

A. 1/55

B. 9/55

C. 18/55

D. 27/55

E. 54/55

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charlie-23 · Answer

Green - 8
Orange - 4
Select 3 one after other with no replacement
So, possible ways of selecting 3 bins = 12*11*10

probability that at least one green bin is selected = 1- no green bin selected 
No green bin selected = all 3 are orange bins
Ways of doing that = 4*3*2

Required Probability = 1- 4*3*2/12*11*10

= 54/55

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Paras96 · Answer

The only items on a shelf are 8 green bins and 4 orange bins. If 3 bins are to be selected from the shelf, one after the other, at random and without replacement, what is the probability that at least one green bin is selected?

Probability = Favorable outcomes / Total outcomes

Total Outcomes = 12C3

Favorable outcomes = Total outcomes - No. of ways no green bin is selected = 12C3 - 4C3

Probability = 12C3 - 4C3 / 12C3 = 54/55

Hence E

youcouldsailaway · Answer

Solving this by only applying principles of probability:
 
\frac{3!}{2!} * \frac{8}{12} * \frac{7}{11} * \frac{4}{10} +
\frac{3!}{2! } * \frac{8}{12} * \frac{4}{11} * \frac{3}{10} +
\frac{3!}{3!} * \frac{8}{12} * \frac{7}{11} * \frac{6}{10} 
 = \frac{54}{55}

Logic here is that there are three cases which would allow at least one green bin to be selected - 1G bin, 2G bins and 3G bins (Remaining bins being selected as per remaining quantity). To quote Bunuel from another thread, we are multiplying by 3!2! each time since GRR scenario could occur in 3 ways: GRR, RGR, or RRG (the number of permutations of 3 letters GXX out of which 2 X's are identical), and so on for each case.

The only items on a shelf are 8 green bins and 4 orange bins. If 3

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The only items on a shelf are 8 green bins and 4 orange bins. If 3

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards