You are dealt 5 cards from a standard 52 card deck Find the

You are dealt 5 cards from a standard 52 card deck. Find the probability that you are dealt all face cards?

Solution

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 CARDS      
K = number of successes in the population =    12 face cards      
n = sample size =    5      
x = number of successes in the sample =    5      
          
Thus,          
          
P(   5   ) =    0.000304737 [ANSWER]