AMC 8 1995 Problem 20

Diana and Apollo each roll a standard die obtaining a number at random from $1$ to $6$. What is the probability that Diana's number is larger than Apollo's number? $\text{(A)}\ \dfrac{1}{3} \text{(B)}\ \dfrac{5}{12} \text{(C)}\ \dfrac{4}{9} \text{(D)}\ \dfrac{17}{36} \text{(E)}\ \dfrac{1}{2}$