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 My solution by ajosin)

We can check the solution without doing a simulation,

a) Combinations with 3 of the same suit are 13*12*11*39*38*10*4

b) Combinations with 4 of the same suit are 13*12*11*10*39*5*4

c) Combinations with 5 of the same suit are 13*12*11*10*9*1*4

d) Combinations 2 of one suit, 2 of another, and 1 of another are, 13*12*13*12*26*30*6 (we need a 6 instead of a 4 at the end because the two double suits can be selected in 6 different ways)

e) Combinations whith two cards of one suit and one of each other suit are, 13*12*13*13*13*60*4

Any 5 cards fall in one and only one of the categories in a)-e), therefore a)-e) represent all possible 5 card combinations and should add up  52*51*50*49*48. They do indeed. Here is their probabilty distribution,

a) 32.6%
b) 4.3%
c) 0.2%
d) 36.5%
e) 26.4%

Posted by ajosin on 2005-03-03 15:30:44