I have a drawer with 6 forks, 6 spoons, and 6 knives in it. If I reach in and randomly remove three pieces of silverware, what is the probability that I get one fork, one spoon, and one knife?
First, we can find the denominator of our fraction.  There are a total of $\dbinom{18}{3}=816$ ways to choose 3 pieces of silverware out of 18.  To find the numerator, we need to count the number of ways to choose one piece of each type of silverware.  There are 6 ways we could choose a fork, 6 ways to choose a spoon, and 6 ways to choose a knife, making a total of $6\cdot 6 \cdot 6=216$ ways to choose a fork, a knife, and a spoon so our final probability is $\frac{216}{816}=\boxed{\frac{9}{34}}$.