According to the rules of 8 ball pool one opponent will pick one type (solid/stripe) and the other opponent will have the other type. For one opponent (Nelson) then to hit and sink both types of balls and keep playing would not actually happen.
When Tony (Larry Hagman) goes to see General Fitzhugh (Jim Backus) as he is playing pool, twice the General struck a numbered ball with his cue stick rather than striking the cue ball first.