i.e. 1 + A+ B + AB = (A + 1)(B + 1) = 3*37

As A, B are positive integers, both the terms (A+ 1) and (B+ 1) are greater than or equal to 2. Also they are factors of 111.
So required number of ordered pairs of positive integers (A, B) = (number of positive integral divisors of 11) – 2 = 4-2 = 2 .