# Regarding methods of enumeration in probability: Bridge (card game)

What is the probability of drawing a hand of 5 spades, 4 hearts, 2 clubs, and 2 diamonds in bridge? I believe the answer is: $$\frac{\binom{13}{5}\binom{13}{4}\binom{13}{2}\binom{13}{2}}{\binom{52}{13}}\approx .0081639$$

The answer in the back of the book is .00882. Am I doing something wrong, or is this a typo?

A bridge hand is a uniform random selection of $13$ cards from a deck of 52 cards. The deck has $13$ cards of each suit.

• I computed the value you've given on the left side and got the value $0.008816390036657731$, which does not equal your value on the right. You appear to have dropped an $8$. Jan 17 '16 at 14:06
• Please specify the rules, amounts and restrictions (instead of relying on math community to know Bridge). Jan 17 '16 at 14:11
• I've added a description for the OP, @barakmanos . Jan 17 '16 at 14:14
• @ThomasAndrews: Thanks :) Jan 17 '16 at 14:17

## 1 Answer

Your formula is correct. The answer I obtained from R is 0.00881639 which agrees with the book's answer. Seemingly your answer has a typo - missing the 8 in the 2nd significant digit.