Also I need to know the calculations involved in the followi

Also, I need to know the calculations involved in the following notation:

Solution

For 2 Aces:

Note that the probability of x successes out of n trials is          
          
P(x) = C(N-K, n-x) C(K, x) / C(N, n)          
          
where          
N = population size =    52      
K = number of successes in the population =    4      
n = sample size =    13      
x = number of successes in the sample =    2      
          
Thus,          
          
P(   2   ) = C(48,11) C(4,2)/C(52,13) =   0.213493397

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For 3 aces:

Note that the probability of x successes out of n trials is          
          
P(x) = C(N-K, n-x) C(K, x) / C(N, n)          
          
where          
N = population size =    52      
K = number of successes in the population =    4      
n = sample size =    13      
x = number of successes in the sample =    3      
          
Thus,          
          
P(   3   ) = C(48,10) C(4,3)/C(52,13)   0.04120048

************

Hence,

P(2 or 3 aces) = C(48,11) C(4,2)/C(52,13) + C(48,10) C(4,3)/C(52,13) = 0.254693877 [ANSWER]