A jar contains only red, yellow, and orange marbles. If there are 3 re

For me, combinations work better.
Ways for selecting 2 yellow marbles out of 5: 5C2
Ways for selecting 1 red marble out of 3: 3C1
Total no. of way for selecting 3 out of 12: 12C3
Probability: 5C2*3C1/12C3=3/22

I started by finding the 2 probabilities, without calculation, like this:
P(YYR)
P(YRY)
P(RYY)

I calculated the first one and ended in 1/22. I looked at the answer choices at this point and saw answer D: 3/22.

This helped me realise that for the 3 possible orderings the probabbility is the same. So, it should be (1/22)*(3), which indeed is 3/22.

Hi All,

I'm a fan of any type of Quant or Verbal shortcut that fits a given situation, BUT if you ever find yourself in a situation in which you can't "spot the shortcut", then you have to just get into the question and do the necessary work as efficiently as you can (re: "brute force").

In this question, we have 3 red, 5 yellow and 4 orange marbles. We're asked for the probability of grabbing 2 yellow and 1 red (in some order)?

There are 3 outcomes that satisfy this question:
YYR
YRY
RYY

Let's calculate each:
YYR = (5/12)(4/11)(3/10) = 60/1320

YRY = (5/12)(2/11)(4/10) = 60/1320

RYY = (2/12)(5/11)(4/10) = 60/1320

Total = 180/1320 = 18/132 = 6/44 = 3/22

Final Answer:

GMAT assassins aren't born, they're made,
Rich

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