Question 4
Jen enters a lottery by selecting $4$ distinct elements of $S = \{1, 2, 3, \ldots, 9, 10\}.$ Then four elements of $S$ are drawn at random. Jen wins a prize if at least two of her numbers were drawn, and wins the grand prize if all four of her numbers were drawn. The probability that Jen wins the grand prize given that Jen wins a prize is $\frac{m}{n}$ where $m$ and $n$ are relatively prime positive integers. Find $m + n.$