Positive integers a, b, and c are randomly and independently selected with replacement from the set \{1,2,3, \ldots, 2010\}. What is the probability that a b c+ a b+a is divisible by 3 ?

**Answer Choices**

A. \dfrac{1}{3}

B. \dfrac{29}{81}

C. \dfrac{31}{81}

D. \dfrac{11}{27}

E. \dfrac{13}{27}