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

Start with the probibility that the first three cards are hearts and the other two are not. That's (13/52)*(12/51)*(11/50)*(39/49)*(38/48). But this must be multiplied by C(5,3) as any three, not just the first three, could be the hearts.  Then it must be multiplied by 4, as it could be any suit, not just hearts.

It all comes out to  2717/8330 = approx. 0.3261704681872749076.

For curiosity's sake, The probability of exactly four cards being of the same suit is

(13/52)*(12/51)*(11/50)*(10/49)*(39/48)*4*C(5,4) = 143/3332 = 0.0429171668667466981

and five as

33/16660 = 0.0019807923169267705.

 

Posted by Charlie on 2005-03-03 14:50:05