Mock AMC 8 #1 - Problem 8

Eric chooses two distinct integers a and b between 1 and 10, inclusive. What is the probability that \gcd(a, b) = 1?

(\textbf{A})\;\dfrac{32}{45}\quad(\textbf{B})\;\dfrac{2}{3}\quad(\textbf{C})\;\dfrac{31}{45}\quad(\textbf{D})\;\dfrac{31}{46}\quad(\textbf{E})\;\dfrac{7}{9}

Enter your answer as a capital letter.