Five cards are drawn from a pack of 52 cards. What is the probability that exactly three of them are of the same suit.
Three cards of a particular suit suit give (13*12*11) combinations.
The other two cards from a different suit form 39*38 combinations.
When we intermix the two sets this can be done in 5!/(3!2!) = 10 ways.
There are (4) posible suits.
The total number of
possible combinations of 5 cards with exactly three of the same suit is
therefore, (13*12*11)*(39*38)*(10)*(4),
which divided by the toal number of 5 card combinations (52*51*50*49*48) gives a probability of 32.6%.
Edited on March 3, 2005, 2:37 pm

Posted by ajosin
on 20050303 14:37:04 