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? by jduval)

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