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!


Call the decks Deck 1 and Deck 2, and imagine cards from the two decks are distinguishable.

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.

  • $\begingroup$ You're a legend for me @Andre.Thank you so much :-) $\endgroup$ – user220382 Jul 3 '16 at 17:26
  • 1
    $\begingroup$ @ZOZ: You are welcome. You had the basic strategy right, and part but not all of the count of favourables. $\endgroup$ – André Nicolas Jul 3 '16 at 17:32
  • $\begingroup$ @AndréNicolas How can chat rooms be closed/deleted ? $\endgroup$ – Peter Jul 3 '16 at 17:58
  • 1
    $\begingroup$ @Peter: Sorry, I do not know. Only used chat 3 times, disliked it intensely. $\endgroup$ – André Nicolas Jul 3 '16 at 18:00

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy