there are 3 identical red balls, 4 identical blue balls, and 5 identical green balls. Three balls are randomly chosen from the bag without replacement. What is the probability that all three of them have different colors?
We have to choose 1 of each color so
\(p= \dfrac{\dbinom{3}{1}\dbinom{4}{1}\dbinom{5}{1}}{\dbinom{12}{3}} = \dfrac{3\cdot 4\cdot 5}{220}=\dfrac{3}{11}\)
