Probability of Matching Words
Combinatorics
Robert and Justy play a game: Robert forms a four-letter word where each letter comes from the set $$\{A,B,C,D,E,F,G,H\}$$without repetition. Justy then guesses the word by providing another four letter-word using the same rules. Justy wins only when his word matches Robert's. What is the probability that Justy wins?
The answer is in the form $\frac{\alpha}{\beta}$ for coprime integers $\alpha$ and $\beta$. Input the answer as the sum $\alpha +\beta$.