AHSME 1979 Problem 27

An ordered pair $( b , c )$ of integers, each of which has absolute value less than or equal to five, is chosen at random, with each such ordered pair having an equal likelihood of being chosen. What is the probability that the equation $x^ 2 + bx + c = 0$ will not have distinct positive real roots? $\textbf{(A) }\frac{106}{121} \textbf{(B) }\frac{108}{121} \textbf{(C) }\frac{110}{121} \textbf{(D) }\frac{112}{121} \textbf{(E) }\text{none of these}$