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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.

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    $\begingroup$ 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 $8$. $\endgroup$ – Thomas Andrews Jan 17 '16 at 14:06
  • $\begingroup$ Please specify the rules, amounts and restrictions (instead of relying on math community to know Bridge). $\endgroup$ – barak manos Jan 17 '16 at 14:11
  • $\begingroup$ I've added a description for the OP, @barakmanos . $\endgroup$ – Thomas Andrews Jan 17 '16 at 14:14
  • $\begingroup$ @ThomasAndrews: Thanks :) $\endgroup$ – barak manos Jan 17 '16 at 14:17
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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.

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