Yes, that's correct.

Now, you just need to get the probability that Alice gets an ace and a normal card, after Darren picked his two cards. The total number of aces is then 3, the number of picture cards is 11 and the number of normal cards is 40, for a total of 50 cards left in the pack.

Multiply the probabilities in the case of Darren and Alice together to get the intersection you're looking for.