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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