+0

# counting problem

0
186
1

In American football, a touchdown scores 7 points, a field goal scores 3 points, and a safety scores 2 points. If a team scored a total of \(10\) points, how many combinations of plays is possible? The order of the plays does not matter, so touchdown and field goal in either order is considered the same combination.

May 21, 2022

#1
0

In American football, a touchdown scores 7 points, a field goal scores 3 points, and a safety scores 2 points. If a team scored a total of 10 points, how many combinations of plays is possible? The order of the plays does not matter, so touchdown and field goal in either order is considered the same combination.

In American football, a touchdown scores 6 points, and the scoring team has the option to try for 1 extra point (kick ball over goalpost) or 2 extra points (run or pass ball into end zone).  The team is not entitled to attempt the point after touchdown without first scoring the touchdown.

6 + 1 + 3                   TD + 1 pt PAT + FG

6 + 2 + 2                   TD + 2 pt PAT + Safety

6 + 2 + 2                   TD + 2 Safeties

3 + 3 + 2 + 2              2 FG + 2 Safeties

2 + 2 + 2 + 2 + 2        5 Safeties

.

May 22, 2022