Probability of a Product Divisible by a Number

From the list of the ten multiples of 5 from 1 to 50 with each multiple listed only once, two are chosen at random without replacement. What is the probability that their product is divisible by 100? The answer is in the form $\frac{\alpha}{\beta}$ where $\alpha$ and $\beta$ are coprime positive integers. Input the value of $\alpha + \beta$.