Fielding practice The coach of a Little League team made up

Fielding practice

The coach of a Little League team made up a game called fielding practice. A player got 10 points for catching a pop fly and making a good throw, 8 points for catching a pop fly and making a bad throw, 7 points for fielding a grounder and making a good throw, 5 points for fielding a grounder and making a bad throw, and 1 point for a good throw after making a catching error ( on either a pop fly or grounder). He scored 20 points in this game. In how many ways could he have scored 20 points?

Solution

There are many possible combinations listed below-

10 + 10 = 20

10 + 8 + 1 + 1 = 20

10 + 7 + 1 + 1 + 1 = 20

10 + 5 + 5 = 20

10 + 5 + 1 + 1 + 1 + 1 + 1 = 20

10 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 = 20

8 + 8 + 1 + 1 + 1 + 1 = 20

8 + 7 + 5 = 20

8 + 7 + 1 + 1 + 1 + 1 + 1 = 20

8 + 5 + 5 + 1 + 1 = 20

8 + 5 + 1 + 1 + 1 + 1 + 1 + 1 + 1 = 20

8 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 = 20

7 + 7 + 5 + 1 = 20

7 + 7 + 1 + 1 + 1 + 1 + 1 + 1 = 20

7 + 5 + 5 + 1 + 1 + 1 = 20

7 + 5 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 = 20

7 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 = 20

5 + 5 + 5 + 5 = 20

5 + 5 + 5 + 1 + 1 + 1 + 1 + 1 = 20

5 + 5 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 = 20

5 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 = 20

1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 = 20