Determine the number of integer solutions of
x1 + x2 + x3 + x4 -: 32,
where
(a) xi ≥ 0, 1 ≤ i ≤ 4
(b) xi > 0, 1 ≤ i ≤ 4
(c) x1, x2 ≥ 5, x3, x4 ≥ 7
(d) xi ≥ 8, 1 ≤ i ≤ 4
(e) xi ≥ - 2, 1 ≤ i ≤ 4
(f) x1, x2, x3 > 0, 0 < x4 < 25