5. Consider the equation x₁ + x₂ + x3 = 18, where 2₁, 22, and 23 are integers. How many solutions are there (a) if #1, #2, 3 ≥ 0? (b) if 21, 22, 232≥ 1? (c) if 0 ≤ ₁ ≤ 3, x₂ ≥ 0, #3 ≥ 0?

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