Question: a) Let n and r be positive integers. Explain why the number of solutions of the equation x1 + x2 +···+ xn = r, where xi is a nonnegative integer for i = 1, 2, 3,...,n, equals the number of r-combinations of a set with n elements.
b) How many solutions in nonnegative integers are there to the equation x1 + x2 + x3 + x4 = 17?
c) How many solutions in positive integers are there to the equation in part (b)?