4 darts are thrown at the target. If each dart hits the target, How many different point totals are possible?

10

To determine the different point totals possible when 4 darts are thrown at the target, we need to consider the scoring system for the darts. Let's assume that the target has a bullseye worth 50 points and an outer ring worth 25 points. There are also different sectors on the target that have varying point values.

To calculate the different point totals, we will use a combination of the possible scores for each dart. Let's break the calculation down:

For the first dart, there are multiple possible scores it can achieve.
- It can hit the bullseye (50 points).
- It can hit the outer ring (25 points).
- It can hit any of the numbered sectors with their respective point values (e.g., 1, 2, 3, etc.).

For the second dart, there are also multiple possible scores it can achieve.
- It can hit the bullseye (50 points).
- It can hit the outer ring (25 points).
- It can hit any of the numbered sectors with their respective point values.

The same goes for the third and fourth darts.

To determine the total number of different point totals, we need to calculate the different combinations of scores for each dart. Since there are multiple possibilities for each dart, we multiply the number of possibilities for each dart together.

Let's look at the numbers:
- For the first dart, there are 52 (50 + 1-20 + 3*0) possible scores (assuming there are 20 numbered sectors).
- For the second dart, there are also 52 possible scores.
- For the third dart, there are 52 possible scores.
- For the fourth dart, there are 52 possible scores.

Using multiplication, we can calculate the total number of different point totals:
52 * 52 * 52 * 52 = 7,311,616

Therefore, there are 7,311,616 different point totals possible when 4 darts are thrown at the target.