For items 1-10, consider the following: The members of Math Club are to choose a representative among four candidates, M, A, T, H. The following table shows the result of the election. Number of votes 18 12 3 First Choice H T M A H T Second Choice M A H A M Third Choice А M H T T H Fourth Choice T H A M M A 1. How many voters choose A as their first choice? 2. Who won the election by plurality? 3. Using the Borda count method and assigning 4 points for the first choice, 3 points for the second choice, 2 points for the third choice and 1 point for the fourth choice, how many points T have received? 4. Using the Borda count method and assigning 4 points for the first choice, 3 points for the second choice, 2 points for the third choice and 1 point for the fourth choice, how many points H have received? 5. Who won the election by Borda count method? 6. Using the plurality with elimination method, who is the candidate to be eliminated in the first round (candidate with the least number of first place votes)? 7. Using the plurality with elimination method, who is the candidate to be eliminated in the second round? 8. Who won the election by plurality with elimination method? 9. Using pairwise comparison method, who won between candidate M and candidate A? 10. Who won the election using the pairwise comparison method?

There are 6 candidates running in a Presidential primary. After each primary, two of the candidates will withdraw, except for the last one, when the winner becomes the nominee.(a) The first primary has all 6 candidates. In how many ways could the 6 candidates finish the race?(b) The second primary will only have the top 4 finishers from the first race. How many ways could the4 candidates finish the second race?(c) The third primary only has the 2 remaining candidates. How many ways could this race finish?(d) Use your answers to parts (a)-(c) to calculate the total number of ways the primaries could play out (that is, how many different ways could the candidates win/lose in the primary)?

F959 - QUESTION 4. BORDA COUNT. The animals get sick and tired of having the Lion be the King of the Jungle, and they overthrow the Lion and hold an election for President of the Jungle. The candidates an the Zebra, the Elephant, the Baboon and the Hyena, and there are 67 voters. The 67 preference lists fall into 6 categories, as summarized below. Using the Borda count method, show the results of the election. 15 Zebra 13 Baboon 12 Zebra 10 Elephant Elephant Hyena 4₂15760 4•13=524.12 48 4.10€ 40 4x936 4×8=33 Hyena Hyena Baboon Hyena Elephant 3-15-45 3-13-39 3·12-30 3·10-30 3x9-27) 3x 8-24 Baboon Zebra Baboon Elephant 1.13 €13/1•12= 12 1·10 = (10) 9 Baboon Zebra Hyena Elephant Elephant Zebra 215- (30) 2.13 (24) 2-12 (24) 2·10 -(20) 2×9=182x8=16) Baboon Zebra 1.15-(15 Hyena 8 1x9 ✓9-9 1x8=8

Adviser to 42 Member local charter of the national mathematics honor society   At the end of the semester, I need to hold elections for a society President, Vice-President, Secretary, Treasurer.  If only 25 of the current members are considered (some are seniors and will be graduating!), how many different slates of officers can I have?