Three marbles are randomly selected, without replacement, from a bag containing two red, three blue and four green marbles. What is the probability that one marble of each color is selected? Express your answer as a common fraction.
We have 2r, 3b, and 4g, marbles(r,b, and g, standing for red, blue, and green.)
The chance that we get a red marble first is 2/9 since the total amount of marbles is 9.
After getting our first marble we now have only 8 left so the chance that we draw a blue marble would be 3/8.
And the chance that we draw a green marble is now 4/7.
To find the probability of drawing all these marbles we have to multiply them by each other:
And drawing these marbles in a different order, for example, green, red then blue still gives: