I've come across a problem in which is necessary to obtain the probability that by drawing 2 cards from a standard deck without replacement, the second card is red.
I understand there are many ways to go about this problem (probably simpler than what I'm asking) but what I'm trying to understand here is not how to obtain the probability, but how to count the number of subsets of the deck that can result in the second card being red.
I think first of all the problem I have is in the book they treat this as a combinations problem. But to me it seems more like a permutations problem since were interested in the event in which the second card is red.
Doesn't this mean that we're interested in all the ordered subsets of S (S containing all cards of the deck) in which the subset contains only 2 elements (cards) and the second element is part of the subset of (Diamonds union Hearts)?