Consider this situation:
You have two standard decks merged together (104 cards). You give 10 cards to each of 4 players. What is the probability that the next time you deal (after the deck is randomly shuffled), everyone gets the same hand they got last turn? Just one person gets the same hand they got last turn?
My approach was something along 104 choose 40 (for everyone getting the same card) or 104 choose 10 (for one person getting the same card), but in my approach I'm not considering the duplicate cards in my deck. I don't think it's 52 choose 40 or 52 choose 10 because then I wouldn't be considering that there is more than one card.
I am very curious about this question and I would love to get an answer. I know its a combinatorics question, but I am unsure of the details.
After posting this question here I got an answer that I don't understand (the longer one). Perhaps someone from the Brilliant community could try to explain it to me? Thank you :)