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Discrete Math : Numbers of Solutions to Equations

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)?
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