Second pair from a 40-card deck missing a pair

A deck has $40$ cards: four copies each of the numbers $1$ through $10$. One pair of cards with the same number is taken out of the deck. Two cards are then drawn at random from the remaining cards. What is the probability that these two cards also have the same number?

$55/703$. After the pair is removed, $38$ cards remain: nine numbers still have four copies and one has two. Matching pairs number $9\binom42+\binom22=55$ out of $\binom{38}{2}=703$.