Six 6-sided dice are rolled.  What is the probability that exactly two of the dice show a 1 and exactly two of the dice show a 2?  Express your answer as a common fraction.
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Six 6-sided dice are rolled.  What is the probability that exactly two of the dice show a 1 and exactly two of the dice show a 2?  Express your answer as a common fraction.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
\dfrac{5}{162}
Six 6-sided dice are rolled.  What is the probability that exactly two of the dice show a 1 and exactly two of the dice show a 2?  Express your answer as a common fraction.
train