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counting and probability senior

Problem

A palindrome is a nonnegative integer number that reads the same forwards and backwards when written in base 10 with no leading zeros. A 6-digit palindrome is chosen uniformly at random. What is the probability that is also a palindrome?
(A)
(B)
(C)
(D)
(E)
Solution
Let the palindrome be the form in the previous solution which is . It doesn't matter what is because it only affects the middle digit. There are ways to pick and , and the only answer choice with denominator a factor of is .
Final answer
E