SOLUTION: Colby is the producer of the local talent competition show, Homegrown Superstars, and needs to form a panel of judges to evaluate performances. Colby has a list of 6 musicians and

Algebra ->  Permutations -> SOLUTION: Colby is the producer of the local talent competition show, Homegrown Superstars, and needs to form a panel of judges to evaluate performances. Colby has a list of 6 musicians and       Log On


   

Question 1205797: Colby is the producer of the local talent competition show, Homegrown Superstars, and needs to form a panel of judges to evaluate performances. Colby has a list of 6 musicians and 8 actors from which to select the judging panel.
a. How many ways are there for Colby to select 5 judges, if the order does not matter?
b. If Colby randomly selects 5 judges, what is the probability that he will choose 2 musicians and 3 actors?

c. If Colby randomly selects 5 judges, what is the probability that at least one of them will be a actor?

Answer by ikleyn(52778) About Me  (Show Source):
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Colby is the producer of the local talent competition show, Homegrown Superstars,
and needs to form a panel of judges to evaluate performances.
Colby has a list of 6 musicians and 8 actors from which to select the judging panel.
a. How many ways are there for Colby to select 5 judges, if the order does not matter?
b. If Colby randomly selects 5 judges, what is the probability that he will choose 2 musicians and 3 actors?
c. If Colby randomly selects 5 judges, what is the probability that at least one of them will be a actor?
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(a)  C%5B6%2B8%5D%5E5 = C%5B14%5D%5E5 = %2814%2A13%2A12%2A11%2A10%29%2F%281%2A2%2A3%2A4%2A5%29 = 2002 possible combinations.    ANSWER




(b)  C%5B6%5D%5E2%2AC%5B8%5D%5E3%29%2FC%7B14%5D%5E5 = %2815%2A56%29%2F2002 = 0.41958  (rounded).    ANSWER  




(c)  The complementary event is 5 judges with no actors (i.e. all judges are musicians)

     The probability for this complementary event is  P' = C%5B6%5D%5E5%2FC%5B14%5D%5E5 = 6%2F2002 = 0.002997  (rounded).   ANSWER

     Therefore, the probability of the event under the question is 

          1 - P' = 1 - 0.002997 = 0.997003  (rounded).

Solved.