AMC 12 2002a Problem 16

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

$\text{(A)}\ 2/5 \text{(B)}\ 9/20 \text{(C)}\ 1/2 \text{(D)}\ 11/20 \text{(E)}\ 24/25$