SOLUTION: There are 19 nominees for 6 vacancies on a city commission, 8 Republicans and 11 Democrats. (a) How many ways can the vacancies be filled by 2 Republicans and 4 Democrats?

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Question 1031197: There are 19 nominees for 6 vacancies on a city commission, 8 Republicans and 11 Democrats.
(a) How many ways can the vacancies be filled by 2 Republicans and 4 Democrats?

(b) If nominees to fill the vacancies are chosen at random, what is the probability of choosing 2 Republicans and 4 Democrats?
Answer by Edwin McCravy(20059)   (Show Source): You can put this solution on YOUR website!
There are 19 nominees for 6 vacancies on a city
commission, 8 Republicans and 11 Democrats.
(a) How many ways can the vacancies be filled
by 2 Republicans and 4 Democrats? 
(8 Republicans choose 2) times (11 Democrats choose 4) =

8C2×11C4 = 9240

(b) If nominees to fill the vacancies are chosen
at random, what is the probability of choosing
2 Republicans and 4 Democrats? 
9240 ways out of (19 nominees choose 6)

9240÷(19C6) = 9240÷27132 = 

which reduces by 84 to  about 34% of the time.

Edwin
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