Probability on 30 cards deck

label Mathematics
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schedule 1 Day
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30 cards contain 10 hearts 10 diamonds 10 clubs, you are dealt 6 cards at random

1. how many different hands are possible?

2. what is the probability that 6 cards dealt include exactly 4 clubs and exactly 2 diamonds?

Mar 10th, 2015

1. Assume that all suits consist of different cards (for example, ace, 2, 3, 4, 5, ..., 10). Then the number of different hands is the number of combinations of 6 from 30 = C(30, 6) = 30!/(24! * 6!) = 593775.

2. The number of hands that include exactly 4 clubs and exactly 2  diamonds is C(10,4)*C(10,2) = 210*45 = 9450, and the probability of dealing such a hand is 9450/593775 = 6/377 = 0.0159 ...

Mar 11th, 2015

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Mar 10th, 2015
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Mar 10th, 2015
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