In football, teams can score 6 points with a touchdown, 3 points with a field goal or 2 points with…

In football, teams can score 6 points with a touchdown, 3 points with a field goal or 2 points with a safety. Additionally, after a touchdown, teams can score 1 bonus point with a field goal kick or 2 bonus points with a 2-point conversion. The final score of a particular football game was 34 to 21 . · If every touchdown is followed with a successful bonus point attempt (1 or 2 points), how many different scoring combinations could have resulted in the losing team’s 21 points? · If every touchdown is followed with a successful bonus point attempt (1 or 2 points), how many different scoring combinations could have resulted in the winning team’s 34 points?