How many solution does the equation x + y + z = 11 have, where x, y, z are non-negative integers?
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Correct answer: D. 78
Explanation
By the stars-and-bars method, the number of non-negative integer solutions of x₁ + x₂ + ... + xₖ = n is C(n + k − 1, k − 1). Here n = 11 and k = 3, so the count is C(11 + 3 − 1, 3 − 1) = C(13, 2) = (13 × 12) / 2 = 78. Hence the equation has 78 solutions.More Discrete Structures and Optimization questions
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