Probability of a three letter word

We’ve got a sign that consists of 3 latin words and 4 numbers (0-9). What is the probability of the word KIM or TOM to appear?

So this one has truly confused me. I thought that we’ve got 3! ways of creating the first word and 3! ways of creating the second word. So 2*3!. Also we’ve got 23^3 ways of choosing letters.

Is my thinking process correct till now? How am I supposed to count the probability?Any help will be greatly appreciated.