If a, b, and c are distinct numbers, how many solutions are there to the following equation?

How many solutions are there to satisfy the equation: ABC+BCD=CBA where each letter represents one digit?

If we have four positive numbers a, b, c and d, there are six ways to multiply the pairs i.e. a*b, a*c, a*d, b*d and c*d. If we tell you the result of five of them without telling you which one is the product of which pair as 2, 3, 4, 5 and 6.

What is the remaining product?