How many integer solutions are there for x + y + z + w = 15 if x ≥ 3,y > −2, z ≥ 1, w > −3?
Question
Solution 1
To solve this problem, we can use the method of generating functions or the stars and bars method. However, the stars and bars method is more straightforward in this case. Here are the steps:
- Adjust the variables to meet the constraints:
- Since x ≥ 3, let x = x' + 3. Then x' ≥ 0.
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