How many solutions are there to the equation x1 + x2 + x3 + x4 = 25 where xi , i = 1, 2, 3, 4, is a non-negative integer such that

(a) xi 3 for i = 1, 2, 3, 4?

(b) x1 2, x2 3, x3 > 5, x4 > 7?

(c) 2 < x1 5?

(d) 3 < x1 7 and