Question 3
A deck of forty cards consists of four $1$’s, four $2$’s, $\ldots,$ and four $10$’s. A matching pair (two cards with the same number) is removed from the deck. Given that these cards are not returned to the deck, let $\frac{m}{n}$ be the probability that two randomly selected cards also form a pair, where $m$ and $n$ are relatively prime positive integers. Find $m + n.$