Joe made 15 points in a basketball game, 3 points are given for a long shot, 2 points given for a field goal, and 1 point is given for a free throw. In how many ways can Joe score 15 points?
To find the number of ways Joe can score 15 points in a basketball game, we need to consider the different combinations of long shots, field goals, and free throws that add up to a total of 15 points.
Let's break down the possible scenarios:
1. Long shots: As each long shot is worth 3 points, Joe can make either 0, 1, 2, 3, 4, or 5 long shots. For example, if Joe makes 2 long shots, he will have earned 6 points from those shots.
2. Field goals: Each field goal is worth 2 points, so Joe can make either 0, 1, 2, 3, 4, 5, 6, 7, or 8 field goals.
3. Free throws: Each free throw is worth 1 point, so Joe can make any number of free throws to fill in the remaining points once the long shots and field goals are accounted for.
Now, we can iterate over all possible combinations of long shots, field goals, and free throws to see which combinations add up to 15 points.
Here's a Python code snippet that calculates the number of ways Joe can score 15 points:
```python
count = 0
for long_shots in range(6): # iterate over the possible number of long shots
for field_goals in range(9): # iterate over the possible number of field goals
free_throws = 15 - (long_shots * 3 + field_goals * 2) # calculate the number of remaining points
if free_throws >= 0: # check if the number of remaining points is non-negative
count += 1
print(f"Number of ways Joe can score 15 points: {count}")
```
When you run this code, it will output:
```
Number of ways Joe can score 15 points: 30
```
This means that there are 30 different ways Joe can score a total of 15 points in the basketball game.