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- 5) There are 4 Biomedical Engineering and 4 Electronics Engineering students running for a student clubelection for 3 empty positions in club board. a. If all of them have an equal chance to be elected, how many different student club boards can be selected? b. If 2 computer engineering and 1 civil engineering students must be in the club board, how many different boards can be selected?There are 4 Biomedical Engineering and 4 Electronics Engineering students running for a student clubelection for 3 empty positions in club board.a. If all of them have an equal chance to be elected, how many different student club boards can beselected? b. If 2 biomedical engineering and 1 electronics engineering students must be in the club board,how many different boards can be selected? c. If Mehmet from Biomedical Engineering and Ali from Electronics Engineering should not be in thesame board, how many different boards can be selected?Last year at a certain high school, 11 students sought the nomination for president of the student body. In how many ways could the voters (student body) rank their first 4 choices?
- A campus club needs to elect four officers: a president, a vice president, a secretary, and a treasurer. The club has five volunteers. Rather than vote individually for each position, the club members will rank the candidates in order of preference. The votes will then be tallied using the Borda Count method. The candidate receiving the highest number of points will be president, the candidate receiving the next highest number of points is vice president, the candidate receiving the next highest number of points is secretary, and the candidate receiving the next highest number of points will be treasurer. Rankings Cynthia 4 2 5 2 3 Andrew 2 3 1 4 5 Jen 5 1 2 3 2 Hector 1 5 4 1 4 Medin 3 4 3 5 1 Number of votes: 9 12 25 24 23 For the preference schedule shown, determine who wins each position in the club. president vice president secretary treasurerSuppose we wish to form a professional development committee with a selection pool of 12 students and 4 faculty. Find the number of different: (i) 5-person committees that can be formed (ii) 5-person committees that can be formed from exactly 2 faculty and 3 students (iii) any size committees that can be formed with an equal number of faculty and studentsOne of the voting methods requires voters to rank all candidates from the most favorable to the least favorable. Each last-place vote receives 1 point, each next-to-last place vote 2 points, and so on. This voting method is called the _________ method. The candidate with the ______ is the winner.
- There are 4 Biomedical Engineering and 4 Electronics Engineering students running for a student clubelection for 3 empty positions in club board.a. If all of them have an equal chance to be elected, how many different student club boards can beselected? b. If 2 biomedical engineering and 1 electronics engineering students must be in the club board,how many different boards can be selected?Consider an election with 301 voters cast for 3 candidates. What is the smallest number of first-place votes that a candidate can receive to win by the Plurality method?In 2012 American Idol completed its 11th season withJennifer Lopez, Steven Tyler, and Randy Jackson asjudges. Although the judges express their opinions aboutthe contestants’ performances, viewers vote to keep theirfavorites in the competition. During each episode, hostRyan Seacrest explains how viewers can vote via text,phone call, or online. Nothing prevents a viewer fromsubmitting multiple votes. Each week the contestant with the lowest number of votes is removed from the com-petition. Why are the results not a true depiction of all Americans’ musical preferences?A) Undercoverage biasB) Voluntary response biasC) The judges’ comments influence voters’ opinions.D) Since some voters may vote multiple times, one votedoes not correspond to one person.E) All of the above.
- The city of Raleigh has 9200 registered voters. There are two candidates for city council in an upcoming election: Brown and Feliz. The day before the election, a telephone poll of 250 randomly selected registered voters was conducted. 80 said they'd vote for Brown, 158 said they'd vote for Feliz, and 12 were undecided.Describe the population actually represented by this surveySUPPOSE THE 18 MEMBERS ON THE BOARD OF THE PROVINCE OF BATANGAS ARE SELECTED ACCORDING TO THE POPULATIONS OF THE 3 CITIES AND 2 BIG TOWNS AS SHOWN BELOW. A. USE THE HAMILTON METHOD TO DETERMINE THE NUMBER OF BOARD MEMBERS EACH CITY AND MUNICIPALITY SHOULD HAVE. B. USE THE JEFFERSON METHOD TO DETERMINE THE NUMBER OF BOARD MEMBER EACH CITY AND MUNICIPALITIES SHOULD HAVE City - Population Batangas - 2,694,335 Tanauan - 173,400 Lipa - 332,386 Lemery - 93,157 Taal - 56,327A chamber of commerce election has 17 candidates for 10 positions. The election consists of two stages. In the first stage, there is an ordered election, with the president being selected first, followed by the vice-president, and then the treasurer, and finally the secretary. In the second stage, the remaining seats are considered 'at large' seats. All the remaining candidates are considered and the 'at large' seats are selected at the same time. How many possible board combinations are there?