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

Okay I came up with about 1/6.  Specifically that is 396/2352. Or 1/5.9393...

Here is how I did it.

First card 52/52.  Second card 51/51.  Third card 50/50.  At this point I assumed the first three cards did not matter, since we only need three to be the same suit.

Fourth card 36/49.  It can be one of three suits 12 of each suit left and there are only 49 cards left in the deck.

Fifth card 11/48.  The last card can be only the suit that you had two of so there are 11 of that suit left and 48 cards in the deck.

Multiply the bolded fractions (most of which are 1) and you have the result.

My only concern is in my assumptions.  It seems as if I assume that the first three cards are different (looking at my math), but I think I accounted for that in first three cards not mattering what suit they were.

Posted by john on 2005-03-03 14:44:32