Probability of drawing all hearts before all spades Let's say we have a 26 card deck(13 hearts and 13 spades), and we want to find the probability that all hearts are drawn before all spades. What is this value? What if we have 52 cards?
For the first case, the way I thought about it was the following. If we have 26 cards, we can arrange them n 26! ways, and if we wanted all the hearts to come before all the spades, this can be done in 13!13! ways since there are 13! ways to arrange each suit of 13 cards. But the answer does not match the probability of 1/2 that is given in the book. I get, 13!13!/26!
The book also mentions that the second probability is also the same. This, I don't understand at all. If someone could please explain to me the answer to this question, as well as why my approach doesn't work, I would be grateful! Thank you so much!

Your answer of $\frac {13!13!}{26!}$ is correct, as is the reasoning you used to get there.  I don't know where $\frac 12$ comes from.  Probably they were answering a different question.
The simple answer to why the $52$ card deck probability is the same is that you can ignore all the other cards.  Deal out the whole deck.  Removing all the clubs and diamonds will not change whether the hearts come before the spades.
