Question 1181307: Robert and frank were shooting baskets. They scored 3 points for a long shot, 2 points for a regular basket and 1 point for a free throw.
1) List all the possible ways Robert could have scored 12 points?
2) What is the possibility of scoring 12 points with a free throw?
3) What is the possibility of scoring 12 points without a free throw?
Answer by greenestamps(13200)   (Show Source):
You can put this solution on YOUR website!
1) List all the possible ways Robert could have scored 12 points.
There is no value added in making a list of all the possible ways. I'll leave that to you.
There IS added value in seeing a logical way to determine the number of different ways 12 points could be scored. And making the complete list will be easy once that is done.
Note the following method can be used to logically make a count of the number of ways of using any set of three numbers to get a particular total.
(i) 4 3-point shots: 1 way
The 4 3-point shots is the whole 12 points; the number of 2-point shots must be 0
(ii) 3 3-point shots: 2 ways
The 3 3-point shots are 9 of the 12 points; there are 3 points left. The number of 2-point shots can be either 0 or 1
(iii) 2 3-point shots: 4 ways
The 2 3-point shots are 6 of the 12 points; there are 6 points left. The number of 2-point shots can be any number 0 to 3
(iii) 1 3-point shot: 5 ways
The 1 3-point shot is 3 of the 12 points; there are 9 points left. The number of 2-point shots can be any number 0 to 4
(iii) 0 3-point shots: 7 ways
The 3-point shots are 0 of the 12 points; there are 12 points left. The number of 2-point shots can be any number 0 to 6
The total number of ways of scoring 12 points with 3-, 2-, and 1-point shots is 1+2+4+5+7 = 19.
You can easily make the complete list from the above discussion.
2) What is the possibility of scoring 12 points with a free throw?
3) What is the possibility of scoring 12 points without a free throw?
These two questions have no mathematical meaning; "possibility" is not a number in math.
Presumably the questions that are asked should have been the probabilities that, if 12 points were scored, they were scored either with or without a free throw (1-point shot).
Those probabilities can easily be determined by examining the complete list of all 19 ways of scoring 12 points.
I leave that to you also.
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