Probability of getting a mirror image In a suitable font, the letters A, H, I, M, O, T, U, V, W, X, and Y are all mirror images of themselves. A string made from these letters will be a mirror image of itself if it reads the same backward and forward: for example, MOM, YUMMUY, MOTHTOM. If a four-letter string in these letters is chosen at random, what is the probability that this string is a mirror image of itself?
The first two letters can be anything.  

The third letter must be the same as the 2nd.  That's 1/11.

The fourth letter must be the same as the 1st.  That's 1/11.

So the probability is $1/11^2 = 1/121$.
$121 / 11^4$ seems right to me.