a) If n and r are positive integers with n ≥ r, how many solutions are there to
x1+ x2 …+ xr = n,
where each xi 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?
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