1
$\begingroup$

Given 25 cards from a standard 52 playing card deck, what are the odds of holding a full suit? Hoping someone can verify my number. I'm working on developing a game, and can't believe the odds I've come up with: 1 in 800,000,000. Seems a bit high! Thanks for any help.

$\endgroup$
3
$\begingroup$

You have $\binom{52}{25}$ possible outcomes when pulling out 25 cards out of 52.

To have a full suit in 25 cards means that 13 out of these 25 are the same suit and other 12 ''are not of our interest'', meaning that they can be any card left from 39 of different suit. You can choose 13 card from same suit on 4 different ways. So you got $$\displaystyle\frac{4\cdot\binom{39}{12}}{\binom{52}{25}}.$$

$\endgroup$
  • $\begingroup$ Looks like a good analysis, and that puts it at about 1:30,500. Much more likely, Thanks 5216 $\endgroup$ – C. J. Feehan Aug 20 '16 at 22:44

Your Answer

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

Not the answer you're looking for? Browse other questions tagged or ask your own question.