Concept explainers
Committees An investigatory committee in the Kingdom of Utopia consists of a chief investigator (a Royal Party member), an assistant investigator (a Birthday Party member), two at-large investigators (either party), and five ordinary members (either party). Royal Party member Larry Sifford is hoping to avoid serving on the committee unless he is the Chief Investigator and Otis Taylor, a Birthday Party member, is the Assistant Investigator. The committee is to be selected at random from a pool of 12 candidates (including Larry Sifford and Otis Taylor), half of whom are Royal Party and half of whom are Birthday Party.
a. How many different committees are possible? [HinT: See Example 5.]
b. How many committees are possible in which Larry’s hopes are fulfilled? (This includes the possibility that he’s not on the committee at all.)
c. What is the probability that he’ll be happy with a randomly selected committee?
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Finite Mathematics and Applied Calculus (MindTap Course List)
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