Question: The three finalists for an award are A, B, and C. They are rated by two judges. Each judge assigns the ratings 1 for best,

The three finalists for an award are A, B, and C. They are rated by two judges. Each judge assigns the ratings 1 for best, 2 for intermediate, and 3 for worst. Let X denote the total score for finalist A (the sum of the ratings received from the two judges).
(a) List all pairs of ratings that finalist A can receive.
(b) List the distinct values of X.

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