2002 AMC 10A Problem 24

Tina randomly selects two distinct numbers from the set $\{1, 2, 3, 4, 5\}$, and Sergio randomly selects a number from the set $\{1, 2, ..., 10\}$. The probability that Sergio’s number is larger than the sum of the two numbers chosen by Tina is

$\text{(A)}\ \dfrac25 \qquad \text{(B)}\ \dfrac9{20} \qquad \text{(C)}\ \dfrac12 \qquad \text{(D)}\ \dfrac{11}{20} \qquad \text{(E)}\ \dfrac{24}{25}$