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Counting & ProbabilityMediumIdentities and Techniques, Proved

Identities and Techniques, Proved · Medium problem

How many ordered triples of integers (x,y,z)(x,y,z) satisfy x+y+z=20x+y+z=20 with x≥2x\ge 2, y≥3y\ge 3 and z≥0z\ge 0?