(a) If n and r are positive integers with n ≥ r, how many solutions are there to
x1 + x2 + ... + xr = n
where each xt is a positive integer, for 1 ≤ i ≤ r?
(b) In how many ways can a positive integer n be written as a sum of r positive integer summands (1 ≤ r ≤ n) if the order of the summands is relevant?