Up until recently, there were five types of scores in the National Football league: safety, worth 2 points; field goal, worth 3 points; touchdown without conversion, worth 6 points; touchdown with 1-point conversion, worth 7 points; and touchdown with 2-point conversion, worth 8 points. Using these types of scores only, answer the following. *Without regard to order, how many ways were there to make 61 of these five types of scores in a game if the number of safeties had to be a single digit prime number, the number of field goals had to be at least 2, the number of touchdowns without conversion could not exceed 4, the numer of touchdows with 1-point conversions had to be odd, and the number of touchdowns with 2-point conversions had to be even?
(Discrete Mathematics)
Up until recently, there were five types of scores in the National Football league: safety, worth 2 points; field goal, worth 3 points; touchdown without conversion, worth 6 points; touchdown with 1-point conversion, worth 7 points; and touchdown with 2-point conversion, worth 8 points. Using these types of scores only, answer the following. *Without regard to order, how many ways were there to make 61 of these five types of scores in a game if the number of safeties had to be a single digit prime number, the number of field goals had to be at least 2, the number of touchdowns without conversion could not exceed 4, the numer of touchdows with 1-point conversions had to be odd, and the number of touchdowns with 2-point conversions had to be even?
(Discrete Mathematics)
*Without regard to order, how many ways were there to make 61 of these five types of scores in a game if the number of safeties had to be a single digit prime number, the number of field goals had to be at least 2, the number of touchdowns without conversion could not exceed 4, the numer of touchdows with 1-point conversions had to be odd, and the number of touchdowns with 2-point conversions had to be even?
(Discrete Mathematics)
Total 5 ways we can get 61 points
1st way:safty 2 - 4 points,field goal 2 - 6 points,touchdown with out conversion 2-12 points,touchdown with conversion one 1-7 points,touchdown with conversion two 4- 32 points
2ndway:safty 2 - 4 points,field goal 4 - 12 points,touchdown with out conversion 1-6 points,touchdown with conversion one 1-7 points,touchdown with conversion two 4- 32 points
3rd way:safty 3 - 6 points,field goal 2 - 6 points,touchdown with out conversion 2-12 points,touchdown with conversion one 3-21 points,touchdown with conversion two 2- 16 points
4th way:safty 3 - 6 points,field goal 4 - 12 points,touchdown with out conversion 1-6 points,touchdown with conversion one 3-21 points,touchdown with conversion two 2- 16 points
5th way:safty 5 - 10 points,field goal 2 - 6 points,touchdown with out conversion 1-6 points,touchdown with conversion one 1-7 points,touchdown with conversion two 4- 32 points
in each way we can get total 61 points
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