Question: (a) Determine the number of nonnegative integer solutions to the pair of equations x1 + x2 + x3 = 6. x1 + x2 + ...

(a) Determine the number of nonnegative integer solutions to the pair of equations
x1 + x2 + x3 = 6. x1 + x2 + ... + x5 = 15.
xi ≥ 0, 1 ≤ i ≤ 5.
(b) Answer part (a) with the pair of equations replaced by the pair of inequalities
x1 + x2 + x3 ≤ 6. x1 + x2 + ... + x5 = 15.
xi ≥ 0, 1 ≤ i ≤ 5.

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