Probability a Number Exceeds a Sum
Combinatorics · problem by Russelle G.
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?
The answer is in the form $\frac{\alpha}{\beta}$ for coprime integers $\alpha$ and $\beta$. Input the answer as the sum $\alpha +\beta$.