Final answer:
In a basketball game, a player can score 7 points through various combinations including 1-point free throws, 2-point field goals, and 3-point field goals, with a total of six different scoring combinations possible to reach exactly 7 points.
Step-by-step explanation:
If a player has 7 points in a basketball match, the possible combinations of points made could be through scoring field goals (which can be either 2 points or 3 points, typically) and free throws (1 point each). Since we're looking for all unique combinations that add up to 7, we can organize them systematically:
- Seven 1-point shots
- One 2-point shot and five 1-point shots
- Two 2-point shots and three 1-point shots
- Three 2-point shots and one 1-point shot
- One 3-point shot and two 1-point shots
- One 3-point shot, one 2-point shot, and one 1-point shot
Note that we do not consider a situation where a player makes more than one 3-point shot since the maximum number possible while still achieving exactly 7 points is one 3-point shot.