KöMaL 2019 B5029

Assume that a certain football team have played 1000 games altogether, and scored 1000 points altogether since the team was founded. (A team score 3 points for every game they win, 1 point for a draw and no points for games they lose.) Prove that there are at most ${(2.9)}^{1000}$ possible sequences of the 1000 scores.