How many integral solutions are there to x + y + z + w = 29, where x ≥ 1, y ≥ 2, z ≥ 3 and w ≥ 0?
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Correct answer: B. 2600
Explanation
Substitute x′ = x − 1, y′ = y − 2, z′ = z − 3: x′ + y′ + z′ + w = 23 with all ≥ 0. Stars and bars: C(23 + 3, 3) = C(26, 3) = 2600.
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