Five cards are drawn from a pack of 52 cards. What is the probability that exactly three of them are of the same suit.

The probability of drawing X number of cards of the same suit is when you draw N cards from a 52 card deck is as follows:

(13 nCr X)*(39 nCr (N-X)) / (52 nCr N)

That is the probability to draw only one suit. If you want 4 suits, simply multiply it by 4.

So for this example:

4*[(13 nCr 3)*(39 nCr 2) / (52 nCr 5)]=32.61704682%

Posted by Marc on 2005-10-19 22:47:32