AMC 12 2010b Problem 11

A palindrome between $1000$ and $10,000$ is chosen at random. What is the probability that it is divisible by $7$?

\textbf{(A)}\ \dfrac{1}{10} \textbf{(B)}\ \dfrac{1}{9} \textbf{(C)}\ \dfrac{1}{7} \textbf{(D)}\ \dfrac{1}{6} \textbf{(E)}\ \dfrac{1}{5}