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counting and probability intermediate

Problem

Three marbles are randomly selected, without replacement, from a bag containing two red, two blue and two green marbles. What is the probability that one marble of each color is selected? Express your answer as a common fraction.
Solution
First, we can find the denominator of our fraction. There are a total of ways to choose 3 marbles out of 6. To find the numerator, we need to count the number of ways to choose one marble of each color. There are 2 ways we could choose a red marble, 2 ways to choose a blue, and 2 ways to choose a green, making a total of ways to choose one marble of each color. Our final probability is .
Final answer
\frac{2}{5}