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)?
The Number of Solutions to Equations is investigated. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.