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Triplets Adam, Bruce, and Charlie enter a triathlon. If there are 9 competitors in the triathlon, and medals are awarded for first, second, and third place, what is the probability that at least two of the triplets will win a medal?
A. 3/14
B. 19/84
C. 11/42
D. 15/28
E. 3/4
Manhattan Advanced Gmat Quant Work out set1 4th question
Using Probability:
P(No triplets win the medals) \(= \frac{(6*5*4)}{(9*8*7)} = \frac{5}{21}\)
P(Only one of the triplets wins a medal) \(= \frac{3*3*6*5}{(9*8*7)} = \frac{15}{28}\)
We multiply by 3 to select one of the 3 triplets and then multiply by 3 to select one of the 3 positions and give it to the triplet selected.
Required Probability \(= 1 - \frac{5}{21} - \frac{15}{28} = \frac{19}{84}\)
Answer (B)Video on Probability:
https://youtu.be/0BCqnD2r-kY