Forgetful distribution

Algebra Level 4

When first introduced to multiplication in algebra, a common mistake made by students is to claim that $a \times ( b + c) = a\times b + c,$ because they forget to distribute $a$ properly. For how many ordered triples of integers $(a, b, c)$ , each of which are between 0 and 10 inclusive, do we actually have $a \times ( b + c) = a\times b + c?$