There are two cases here:
Case 1: First card chosen is a queen
452∗351=1221452∗351=1221Case 2: First card chosen is not a queen.4852∗451=162214852∗451=16221Adding both the cases, we get 1722117221 = 452452 = 113113In a simpler case: Think about it this way: Shuffle a deck of cards randomly. The probability of drawing a queen as your second card is the same as the probability that the second card in the deck is a queen, which is clearly 4/52.