If a, b, c are three natural numbers in A.P. such that a + b + c = 21, then the possible number of values of a, b, c is

Let b = a + d and c = a + 2d.Given: a + a + d + a + 2d = 21 ⇒ a + d = 7∴ a + c = 14 and b = 7Now, the number of positive integral solutions of a + c = 14 is equal to coefficient of x14 in (x + x2 + x3 +….)2 = Coefficient of x12 in (1 + x + x2 …)2 = 13C12 = 13.