# Math Help - Bridge Game Probability/Combination Problem Help

1. ## Bridge Game Probability/Combination Problem Help

The four players in a game of bridge are called North, South, East, and West. What is the probability that East and West have no diamonds? (I.e., what is the probability that all of the diamonds are held by North and South?)

Ok here is my try -
Each of the player has 13 cards. So North and South has a total of 26 cards. There are 13 diamonds. So N & S can have all diamonds by - 26C13 and then the remaining 13 cards can be from the remaining 39 cards - 39C13 .

$Total probability = 26C13 * 39C13 / 52C26 = 170.346$ which is wrong answer as probability needs to be between 0 and 1.

We can even do it another way where we select 26 cards for East and West from the 39 cards .
Total Probability = 39C26/52C26 = 1.637*10-5 which is between 0 and 1