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In the card game bridge 52 cards are dealt with an equal chance for all sets of hands of 13 each to East West North and South

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Example 4 (Bridge): In the card game bridge 52 cards are dealt with an equal chance for all sets of hands of 13 each to East West North and South. Given that North and South have a total of 8 spades what is the chance that East has 3 of the remaining 5 spades?the answer is given in the problem (example 4) but i still do not understand the E Fi F and why P(F1) = P(F2) = P(F3) = P(F)/M (check out the attached file)i can understand that there remains totally 26 cards to choose 13 3 out of 5 spades and then 10 out of 21 other cards. then the equation from this condition is (5 choose 3)*(21 choose 10) / (26 choose 13) = 0.339.however why not take the north and south possible cards combination into account which will result in a smaller probability that E has 3 out of 5 spades. different cards combo in north and south hands will result in different cards combo in east right? but i do not know how?0

 
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