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

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.