AIME II 2010 #13

[stupidityismygam]

The 52 cards in a deck are numbered [unparseable or potentially dangerous latex formula]. Alex, Blair, Corey, and Dylan each picks a card from the deck without replacement and with each card being equally likely to be picked. The two persons with lower numbered cards form a team and the two persons with higher numbered cards form another team. Let [unparseable or potentially dangerous latex formula] be the probability that Alex and Dylan are on the same team, given that Alex picks one of the cards [unparseable or potentially dangerous latex formula] and Dyland picks the other of these two cards. The minimum value of [unparseable or potentially dangerous latex formula] for which [unparseable or potentially dangerous latex formula] can be written as [unparseable or potentially dangerous latex formula] where [unparseable or potentially dangerous latex formula] and [unparseable or potentially dangerous latex formula] are relatively prime positive integers. Find [unparseable or potentially dangerous latex formula]