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

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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(53937) (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) = = = 2002 possible combinations. ANSWER (b) = = 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' = = = 0.002997 (rounded). ANSWER Therefore, the probability of the event under the question is 1 - P' = 1 - 0.002997 = 0.997003 (rounded).

Solved.