Q #10: Runners on first and third base with one out. Batter hits a deep fly ball to leftfield which is caught for the second out of the inning. Runner on third base properly tags and then crosses home plate to score. However, the runner on first base was off with the pitch and failed to tag. The defense makes an appeal over at first base (after the runner from third crossed the plate). The umpire calls the runner out at first base for the third out of the inning. Does the run count? You make the call.
A #10: The run counts. When the third out of an inning occurs on an appeal for leaving a base too early, the umpire must determine whether the other runner crossed the plate before or after the appeal. If the runner from third reached home plate before the defense made the appeal, the run counts (as it is a timing play).
If the third out had occurred as result of the batter-runner not reaching first base safely, or had occurred as a result of a force out, the run would not score as those situations do not involve considering the timing of when the runner reached the plate.