SOLUTION: how many different ways can you score 77 points in a football game?

Question 404035: how many different ways can you score 77 points in a football game?
Answer by Edwin McCravy(20081) (Show Source): You can put this solution on YOUR website!


6 points for a touchdown with no extra point kick or conversion.
7 points for a touchdown with an extra point kick.
8 points for a touchdown with a 2-point conversion.
3 points for a field goal.
2 points for a safety.

There are 67 possibilities, including the extremely unlikely
case of #14 below where there are

 1 6-point TDs. no extra point       6 points
 1 TDs with a 2-point conversion     8 points
 1 Field goal                        3 points
30 safeties                         60 points
---------------------------------------------
                                    77 points 

Here they all are:

1. 0 6pt TDs, 0 7pt TDs, 3 8pt TDs, 3 3pt FGs, 22 2pt safeties
2. 0 6pt TDs, 0 7pt TDs, 7 8pt TDs, 7 3pt FGs, 0 2pt safeties
3. 0 6pt TDs, 1 7pt TDs, 2 8pt TDs, 2 3pt FGs, 24 2pt safeties
4. 0 6pt TDs, 1 7pt TDs, 6 8pt TDs, 6 3pt FGs, 2 2pt safeties
5. 0 6pt TDs, 2 7pt TDs, 1 8pt TDs, 1 3pt FGs, 26 2pt safeties
6. 0 6pt TDs, 2 7pt TDs, 5 8pt TDs, 5 3pt FGs, 4 2pt safeties
7. 0 6pt TDs, 3 7pt TDs, 0 8pt TDs, 0 3pt FGs, 28 2pt safeties
8. 0 6pt TDs, 3 7pt TDs, 4 8pt TDs, 4 3pt FGs, 6 2pt safeties
9. 0 6pt TDs, 4 7pt TDs, 3 8pt TDs, 3 3pt FGs, 8 2pt safeties
10. 0 6pt TDs, 5 7pt TDs, 2 8pt TDs, 2 3pt FGs, 10 2pt safeties
11. 0 6pt TDs, 6 7pt TDs, 1 8pt TDs, 1 3pt FGs, 12 2pt safeties
12. 0 6pt TDs, 7 7pt TDs, 0 8pt TDs, 0 3pt FGs, 14 2pt safeties
13. 0 6pt TDs, 11 7pt TDs, 0 8pt TDs, 0 3pt FGs, 0 2pt safeties
14. 1 6pt TDs, 0 7pt TDs, 1 8pt TDs, 1 3pt FGs, 30 2pt safeties
15. 1 6pt TDs, 0 7pt TDs, 5 8pt TDs, 5 3pt FGs, 8 2pt safeties
16. 1 6pt TDs, 1 7pt TDs, 0 8pt TDs, 0 3pt FGs, 32 2pt safeties
17. 1 6pt TDs, 1 7pt TDs, 4 8pt TDs, 4 3pt FGs, 10 2pt safeties
18. 1 6pt TDs, 2 7pt TDs, 3 8pt TDs, 3 3pt FGs, 12 2pt safeties
19. 1 6pt TDs, 3 7pt TDs, 2 8pt TDs, 2 3pt FGs, 14 2pt safeties
20. 1 6pt TDs, 4 7pt TDs, 1 8pt TDs, 1 3pt FGs, 16 2pt safeties
21. 1 6pt TDs, 5 7pt TDs, 0 8pt TDs, 0 3pt FGs, 18 2pt safeties
22. 1 6pt TDs, 7 7pt TDs, 2 8pt TDs, 2 3pt FGs, 0 2pt safeties
23. 1 6pt TDs, 8 7pt TDs, 1 8pt TDs, 1 3pt FGs, 2 2pt safeties
24. 1 6pt TDs, 9 7pt TDs, 0 8pt TDs, 0 3pt FGs, 4 2pt safeties
25. 2 6pt TDs, 0 7pt TDs, 3 8pt TDs, 3 3pt FGs, 16 2pt safeties
26. 2 6pt TDs, 1 7pt TDs, 2 8pt TDs, 2 3pt FGs, 18 2pt safeties
27. 2 6pt TDs, 2 7pt TDs, 1 8pt TDs, 1 3pt FGs, 20 2pt safeties
28. 2 6pt TDs, 3 7pt TDs, 0 8pt TDs, 0 3pt FGs, 22 2pt safeties
29. 2 6pt TDs, 3 7pt TDs, 4 8pt TDs, 4 3pt FGs, 0 2pt safeties
30. 2 6pt TDs, 4 7pt TDs, 3 8pt TDs, 3 3pt FGs, 2 2pt safeties
31. 2 6pt TDs, 5 7pt TDs, 2 8pt TDs, 2 3pt FGs, 4 2pt safeties
32. 2 6pt TDs, 6 7pt TDs, 1 8pt TDs, 1 3pt FGs, 6 2pt safeties
33. 2 6pt TDs, 7 7pt TDs, 0 8pt TDs, 0 3pt FGs, 8 2pt safeties
34. 3 6pt TDs, 0 7pt TDs, 1 8pt TDs, 1 3pt FGs, 24 2pt safeties
35. 3 6pt TDs, 0 7pt TDs, 5 8pt TDs, 5 3pt FGs, 2 2pt safeties
36. 3 6pt TDs, 1 7pt TDs, 0 8pt TDs, 0 3pt FGs, 26 2pt safeties
37. 3 6pt TDs, 1 7pt TDs, 4 8pt TDs, 4 3pt FGs, 4 2pt safeties
38. 3 6pt TDs, 2 7pt TDs, 3 8pt TDs, 3 3pt FGs, 6 2pt safeties
39. 3 6pt TDs, 3 7pt TDs, 2 8pt TDs, 2 3pt FGs, 8 2pt safeties
40. 3 6pt TDs, 4 7pt TDs, 1 8pt TDs, 1 3pt FGs, 10 2pt safeties
41. 3 6pt TDs, 5 7pt TDs, 0 8pt TDs, 0 3pt FGs, 12 2pt safeties
42. 4 6pt TDs, 0 7pt TDs, 3 8pt TDs, 3 3pt FGs, 10 2pt safeties
43. 4 6pt TDs, 1 7pt TDs, 2 8pt TDs, 2 3pt FGs, 12 2pt safeties
44. 4 6pt TDs, 2 7pt TDs, 1 8pt TDs, 1 3pt FGs, 14 2pt safeties
45. 4 6pt TDs, 3 7pt TDs, 0 8pt TDs, 0 3pt FGs, 16 2pt safeties
46. 4 6pt TDs, 6 7pt TDs, 1 8pt TDs, 1 3pt FGs, 0 2pt safeties
47. 4 6pt TDs, 7 7pt TDs, 0 8pt TDs, 0 3pt FGs, 2 2pt safeties
48. 5 6pt TDs, 0 7pt TDs, 1 8pt TDs, 1 3pt FGs, 18 2pt safeties
49. 5 6pt TDs, 1 7pt TDs, 0 8pt TDs, 0 3pt FGs, 20 2pt safeties
50. 5 6pt TDs, 2 7pt TDs, 3 8pt TDs, 3 3pt FGs, 0 2pt safeties
51. 5 6pt TDs, 3 7pt TDs, 2 8pt TDs, 2 3pt FGs, 2 2pt safeties
52. 5 6pt TDs, 4 7pt TDs, 1 8pt TDs, 1 3pt FGs, 4 2pt safeties
53. 5 6pt TDs, 5 7pt TDs, 0 8pt TDs, 0 3pt FGs, 6 2pt safeties
54. 6 6pt TDs, 0 7pt TDs, 3 8pt TDs, 3 3pt FGs, 4 2pt safeties
55. 6 6pt TDs, 1 7pt TDs, 2 8pt TDs, 2 3pt FGs, 6 2pt safeties
56. 6 6pt TDs, 2 7pt TDs, 1 8pt TDs, 1 3pt FGs, 8 2pt safeties
57. 6 6pt TDs, 3 7pt TDs, 0 8pt TDs, 0 3pt FGs, 10 2pt safeties
58. 7 6pt TDs, 0 7pt TDs, 1 8pt TDs, 1 3pt FGs, 12 2pt safeties
59. 7 6pt TDs, 1 7pt TDs, 0 8pt TDs, 0 3pt FGs, 14 2pt safeties
60. 7 6pt TDs, 5 7pt TDs, 0 8pt TDs, 0 3pt FGs, 0 2pt safeties
61. 8 6pt TDs, 1 7pt TDs, 2 8pt TDs, 2 3pt FGs, 0 2pt safeties
62. 8 6pt TDs, 2 7pt TDs, 1 8pt TDs, 1 3pt FGs, 2 2pt safeties
63. 8 6pt TDs, 3 7pt TDs, 0 8pt TDs, 0 3pt FGs, 4 2pt safeties
64. 9 6pt TDs, 0 7pt TDs, 1 8pt TDs, 1 3pt FGs, 6 2pt safeties
65. 9 6pt TDs, 1 7pt TDs, 0 8pt TDs, 0 3pt FGs, 8 2pt safeties
66. 11 6pt TDs, 0 7pt TDs, 1 8pt TDs, 1 3pt FGs, 0 2pt safeties
67. 11 6pt TDs, 1 7pt TDs, 0 8pt TDs, 0 3pt FGs, 2 2pt safeties

Edwin

RELATED QUESTIONS
in a certain football league, the only ways to score are to kick a field goal for 3... (answered by josmiceli)
In how many different ways can 15 tickets to a football game be distributed among a class (answered by nyc_function)
How many different ways can you score an 80 on a 10 question true- false... (answered by graphmatics)
in a poker game how many ways can you form a full house (answered by Alan3354)
MAT 145: Topics In Contemporary Math Trees 4) A football team has three different... (answered by ikleyn)
MAT 145: Topics In Contemporary Math Trees 4) A football team has three different... (answered by ikleyn)
Andrew has a mean score of 18 points per game in his four basketball games of the season. (answered by stanbon)
In a basketball game, Phil scored three times as many points as Fred. Together they... (answered by Cromlix)
Measure of the center of a set of data. The middle school football team wants to average (answered by amarjeeth123)