Question: Problem 5: Integer solutions How many non-negative integer solutions are there of the equation x+y+z = 20 satisfying x 10, y 5, and z 15.

Problem 5: Integer solutions

How many non-negative integer solutions are there of the equation x+y+z = 20 satisfying x 10, y 5, and z 15. Hint: we have seen how to solve this when the constraints are lower bounds, i.e. using > instead of . Let Sx be the set of all solutions in which x > 10. Define Sy and Sz similarly, and find |Sx Sy Sz| and subtract this number from all possible solutions (with only x, y, z 0).

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