The offices of president vice president secretary and treasu

The offices of president, vice president, secretary, and treasurer for an environmental club will be filled from a pool of 14 candidates. Eight of the candidates are members of the debate team. (a) What is the probability that all of the offices are filled by members of the debate team? (b) What is the probability that none of the offices are filled by members of the debate team?

Solution

A)

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 =    12      
K = number of successes in the population =    5      
n = sample size =    4      
x = number of successes in the sample =    4      
          
Thus,          
          
P(   4   ) =    0.01010101 [ANSWER]

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b)

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 =    12      
K = number of successes in the population =    5      
n = sample size =    4      
x = number of successes in the sample =    0      
          
Thus,          
          
P(   0   ) =    0.070707071 [ANSWER]