How many different ways can a team have a final score of 11 points in NFL football?
c'mon - just list them. They can score 2,3,6, with an optional 1 or 2 for every 6-pt touchdown.
To find the number of different ways a team can have a final score of 11 points in NFL football, we can analyze the possible combinations of touchdowns, field goals, and safeties.
1. Touchdowns: A team can score a touchdown worth 6 points. To get a final score of 11 points, the team would need to score exactly one touchdown.
- This gives us one possible way.
2. Field Goals: A team can also score a field goal worth 3 points. To get a final score of 11 points, the team would need to score exactly one field goal.
- This gives us one possible way.
3. Combining Touchdowns and Field Goals: We can explore combinations of touchdowns and field goals to see if they sum up to 11. Note that a team can score at most two touchdowns (12 points) or three field goals (9 points), so we need to check all possible combinations within those limits.
a) One touchdown and one field goal:
- A touchdown (6 points) and a field goal (3 points) sum up to 9 points, which is less than 11. Thus, it's not possible with this combination.
b) Two touchdowns:
- Two touchdowns (2 x 6 points) sum up to 12 points, which is more than 11. Thus, it's not possible with this combination.
c) Three field goals:
- Three field goals (3 x 3 points) sum up to 9 points, which is less than 11. Thus, it's not possible with this combination.
4. Assuming touchdowns and field goals haven't worked, we are left with the possibility of safeties. A safety in the NFL is worth 2 points. We can now explore combinations of safeties to see if they sum up to 11.
a) Five safeties:
- Five safeties (5 x 2 points) sum up to 10 points, which is less than 11. Thus, it's not possible with this combination.
b) Six safeties:
- Six safeties (6 x 2 points) sum up to 12 points, which is more than 11. Thus, it's not possible with this combination.
c) Four safeties:
- Four safeties (4 x 2 points) sum up to 8 points, which is less than 11. Thus, it's not possible with this combination.
d) Three safeties:
- Three safeties (3 x 2 points) sum up to 6 points, which is less than 11. Thus, it's not possible with this combination.
e) Two safeties:
- Two safeties (2 x 2 points) sum up to 4 points, which is less than 11. Thus, it's not possible with this combination.
f) One safety:
- A single safety (1 x 2 points) sums up to 2 points, which is less than 11. Thus, it's not possible with this combination.
Based on the analysis, there is only one possible way for a team to have a final score of 11 points in NFL football: by scoring one touchdown and one field goal.