"If choice X is a winner of an election and, in a reelection, the only changes in the ballots are changes that only favor X, then X should remain a winner of the election." This fairness criterion is called the A) monotonicity B) IIA C) Condorcet D) majority
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- 1. There are seven candidates running for the presidential and vice-presidential nomination. How many ways are there of selecting presidential and vice-presidential candidates from the field? (Assume that every candidate is willing to accept either nomination.)A commitee of 2 teachers is to be formed in a school such that there is one male and one female representative.In how many ways the committee can be formed if there are 15 male teachers and 12 female teachers.Suppose a car you want to buy has five choices for inte-rior colors, three types of radios, three engine choices,two battery types (regular and heavy duty), 10 exterior colors, two transmission choices, and four types of wheel covers. How many possible combinations of thecar are possible for the manufacturer? What can be doneto limit the number of combinations without limitingcustomer choice?
- Many everyday decisions, like who will drive to lunch or who will pay for the coffee, are made by the toss of a (presumably fair) coin and using the criterion "heads, you will; tails, I will." This criterion is not quite fair, however, if the coin is biased (perhaps due to slightly irregular construction or wear). John von Neumann suggested a way to make perfectly fair decisions, even with a possibly biased coin. If a coin, biased so that P(h)=0.5200 and P(t)=0.4800, is tossed twice, find the probability P(hh).1 An academic building consists of three floors. There are 10 offices on each floor including 3 corner offices. If there are 15 faculties in the department out of which 4 of them preferred corner offices, in how many ways can you assign offices to all faculties that agree with their preference?1. A teacher administers a multiple-choice quiz with four questions and four possible answers: a, b, c, and d. What is the bare minimum of students required in the class to ensure that at least three answer sheets are identical?2. What is the minimum number of students from each of the 15 regions who must be enrolled in a university to ensure that there are at least 52 from the same region?
- Among the seven nominees for two vacancies on acity council are three men and four women. In how manyways can these vacancies be filled(a) with any two of the seven nominees;(b) with any two of the four women;(c) with one of the men and one of the women?A manuscript that has been rejected by a journal: a. can be revised and resubmitted b. cannot be resubmitted to the same journal without an invitation from the editor c. can be requested to be re-reviewed by a different set of peers within the same journal d. can be reconsidered if an additional fee is paid7 Assume that the student has a cup with 6 writing implements: 3 pencils, 2 ball point pens, and 1 felt-tip pen. (1) In how many ways can the student select 2 writing implements? (2) In how many ways can the selection be made if no more than one ball point pen is selected?
- In how many ways can the hosts of the ASEAN Summit choose the main judge, secondary judge, and tertiary judge among 3 Filipinos, 4 Chinese, and 6 Vietnamese if:1. The hosts were to choose only Vietnamese and Chinese2. The hosts were to choose only 1 per race Please answer the 2 subparts9. In how many ways can a committee of 6 members be choosen from a group a group of 12membersHow many seating arrangements can be formed if by seating A,B,C,D,E in a row: If A,B,C sit together in this order If A,B,C sit together in any order If E is seated somewhere to the left of D If B and C shouldn't sit together, and neither should E and D If neither A nor C should sit beside B If A shouldn't sit to the immediate left of B, and C shouldn't sit to the immediate right of B If B sits somewhere to the left of E, and E sits somewhere to the right of D