2010 AMC 10B Problem 21

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

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.