2024 AIME I Problem 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.

Leading zeroes must be inputted, so if your answer is 34, then input 034

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