A Football Question

MathStudent1999

Junior Member
Joined
Mar 18, 2012
Messages
76
In professional football, it is possible to score 2, 3, or 6 points. (Safety, Field Goal and Touchdown) If a touchdown a scored it is also possible to score one additional point. The score of a football game was 21 to 17. Find the total number of possible combinations of points to achieve the final score.

Is there a faster way to do it instead of counting the number of ways to get 21, counting the number of ways to get 17 and then multiplying the two together?
 
Is there a faster way to do it instead of counting the number of ways to get 21, counting the number of ways to get 17 and then multiplying the two together?

Golly, I hope so! But I can't think of one. :oops:
 
In professional football, it is possible to score 2, 3, or 6 points. (Safety, Field Goal and Touchdown) If a touchdown a scored it is also possible to score one additional point. The score of a football game was 21 to 17. Find the total number of possible combinations of points to achieve the final score.

Is there a faster way to do it instead of counting the number of ways to get 21, counting the number of ways to get 17 and then multiplying the two together?
Since the "21" and the "17" are independent events, you are going to have to come up with the number of ways separately (and then the multiplication is a simple operation anyhow). I don't think there are any shortcuts. Try to systematize the counting, for instance making a table with columns for with number of 7's, 6's, 3's, 2's.
To make 21:
3 7's
2 7's no way
1 7, 2 6's, 1 2
1 7, 1 6, . . .
 
I got 8 ways to get 17 and 16 ways to get 21. Multiplying the two together I got 128. Is this correct?
 
Top