AMC 12 Mock Exam 1 Problem 7

Problem 7 of 25

A jar contains $4$ red marbles, $3$ blue marbles, and $2$ green marbles. Three marbles are drawn at random from the jar without replacement. What is the probability that the three marbles drawn are all different colors?

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Solution

There are $\binom93=84$ equally likely sets of three marbles. A set with all three colors consists of one red, one blue, and one green marble, and there are $4\cdot3\cdot2=24$ such sets. The probability is $\frac{24}{84}=\boxed{\tfrac27}$ .

Tagged: probability without replacement

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