Five cards are drawn from a pack of 52 cards. What is the probability that exactly three of them are of the same suit.
(In reply to Solution?
Here is were you are missing some probabilty;
The first 4 cards can be two doulbe suits, in wich case the fith card has 22/48.
Thre first 4 cards already have 3 of the same suit, in wich case the fith card has 38/48.
So the last cards probability is somewhere betwenn 11/48 and 38/48, with a naive average (~25/48) we get about twice the probability you originally got and the correct answer (1/3).
But your logic does give a lower limit (we know that the probabilty is higher than 1/6).
Posted by ajosin
on 2005-03-03 15:53:59