I don't understand this:

For the second case, the valid scorecards are {1,1,1}, {0,1,2}, {0,2,1}, {1,0,2}, {1,2,0}, {2,0,1}, {2,1,0}.

For the fourth case, there is no valid scorecard. It is not possible for both players to have score 1.

Why is {1,1,1} valid in 4th case and {1,1} not valid in 2nd?