Answer: There are a total of 7 different point totals possible.
Explanation:
To find the possible point totals, we need to consider all the different combinations of points we can get by hitting one, two, or all three regions of the target.
If we hit only one region, we can get a total of 3, 5, or 7 points.
If we hit two regions, we can pair the 3-point region with either the 5-point region (for a total of 8 points) or the 7-point region (for a total of 10 points). If we pair the 5-point region with the 7-point region, we get a total of 12 points.
If we hit all three regions, we get a total of 15 points.
Therefore, the possible point totals are:
3, 5, 7, 8, 10, 12, and 15.