# The probability that the player gets all distinct cards is?

Two decks of playing cards are well shuffled and 26 cards are randomly distributed to a player. Then, the probability that the player gets all distinct cards is ?

I think the answer should be $$\frac{\binom{52}{26}}{\binom{104}{26}}+(something)$$ because it feels like I could take say 26 cards from one deck only or distinct cards from two decks.I'm not being able to implement the latter case into the answer.Please guide me!

A deck has 52 distinct cards!

here are $\binom{52}{26}$ ways to choose the types of the $26$ cards. For each type, there are $2$ ways to decide whether the card comes from Deck 1 or Deck 2, for a total of $\binom{52}{26}2^{26}$ "favourables."
For the probability, divide as you did by $\binom{104}{26}$, the number of ways to choose $26$ cards from the double deck.