A base-10 three-digit number $n$ is selected at random. What is the probability that the base-9 representation and the base-11 representation of $n$ are both three-digit numerals?
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
A base-10 three-digit number $n$ is selected at random. What is the probability that the base-9 representation and the base-11 representation of $n$ are both three-digit numerals?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
\frac{152}{225}
A base-10 three-digit number $n$ is selected at random. What is the probability that the base-9 representation and the base-11 representation of $n$ are both three-digit numerals?
train