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Find the number of solutions to x1+x2+x3+x4=16 with integers x1 ,x2, x3, x4 satisfying (a)  xj ≥...

Find the number of solutions to x1+x2+x3+x4=16 with integers x1 ,x2, x3, x4 satisfying

(a)  xj ≥ 0, j = 1, 2, 3, 4;

(b) x1 ≥ 2, x2 ≥ 3, x3 ≥ −3, and x4 ≥ 1;

(c) 0 ≤ xj ≤ 6, j = 1, 2, 3, 4

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