Question

In a suitable font, the letters A, H, I, M, O, T, U, V, W, X, 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 as 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? (Round your answer to four decimal places.)

Answer 1

so the first and last places are the same and the middle places are the same

Answer 2

or they can all be same letters

Answer 3

lets get rid off the obvious case first all same letters
there are 11 cases of those

Answer 4

now lets look at the same first and last case

Answer 5

for every same first and last case, there are anotther 10 same letter cases in the middle so
11*10