Parks Committee: In the County of Eagleton, the City Council consists of 15 politicians: 7 of whom are Republicans and the rest democrats. By law, a parks committee must be made which consists of three Republicans and two Democrats. (a) How many ways are there of choosing the members of the committee? (b) Your spouse (Democrat) and you (Republican) decided that if one of you is on the committee, the other one shouldn't be. How many ways can the members be chosen such that this condition is fulfilled? (c) Suppose that we have to specify a Republican to serve as Chair and a Democrat to serve as Ranking Member. How many ways are there of choosing the members of the committee, the Chair, and the Ranking Member?
Parks Committee: In the County of Eagleton, the City Council consists of 15 politicians: 7 of whom are Republicans and the rest democrats. By law, a parks committee must be made which consists of three Republicans and two Democrats.
(a) How many ways are there of choosing the members of the committee?
(b) Your spouse (Democrat) and you (Republican) decided that if one of you is on the committee, the other one shouldn't be. How many ways can the members be chosen such that this condition is fulfilled?
(c) Suppose that we have to specify a Republican to serve as Chair and a Democrat to serve as Ranking Member. How many ways are there of choosing the members of the committee, the Chair, and the Ranking Member?
(d) Suppose the rules are relaxed, and it's required only that the committee NOT consist entirely of Republicans or entirely of Democrats. How many ways of choosing the five members of the committee are there now? (Do not include a Chair and Ranking Member.)
(e) How many anagrams are thereof the word "ELECTION"?
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