You can get 1 point, 2 points, or 3 points. Your team has 7 points. How many different ways could your team have scored those points?

Question

Make a table and explain your work.

Answer 1

In the game of basketball, a player can make a basket for 1, 2, or 3 points.

While a probabilistic solution exists to answer this question , it is a simple matter to understand that if a team has a total of 7 points, that total can be made by considering how many baskets of each type were made.

 

The possible combinations are:

3, 3, 1 -- 3, 2, 2 -- 3, 2, 1, 1 -- 3, 1, 1, 1, 1 -- (4 combinations)

2, 2, 2, 1 -- 2, 2, 1, 1, 1 -- 2, 1, 1, 1, 1, 1  -- (3 combinations)

1, 1, 1, 1, 1, 1, 1 -- (1 combination)

 

So, the answer is 8 combinations.

Answer 2

Ooh, what a poorly worded question! But if each person on a team (not just you!) can get 1, 2, or three points, does that help? Not really, if you take "ways" to mean things like who gets points, and in what order. But if nobody cares about that (did you ever see a team where nobody cared WHO scored the points, though?), then the problem would be, how many ways can you total 7 from integers of the set {1, 2, 3}, reusing integers permitted.

That's {1,1,1,1,1,1,1}, {1,1,1,1,1,2}, {1,1,1,1,3}, {1,1,1,2,2}, {1,1,2,3}, {1,3,3}, {3,4}.

What you've done here is to order the counting number (1,2,3 ...) combinations which total 7, *in increasing size only*, starting from the minimum possible set, and considering the LAST possible position. When you've exhausted the possibilities for a particular position, then you move back one position and start again. This is easy to generate and to check over.

Your problem is to put these possibilities into a table; you'll have to say "Score achieved" or some such, to take up table space for the "shorter lines".