A city has 12 districts. An election is coming up for the city metro council (1 member from each district). In districts 1-5, a single republican and single democrat are running for each district; In districts 6-8, 2 democrats and 2 republicans are running in each district; in district 9, the incumbent (a democrat) is running unopposed. In districts 10-11, 2 republicans and 1 democrat are running in each district. In district 12, 3 democrats and 1 republican are running. a. What is the total number of unique outcomes? b. In how many of these outcomes does one party or the other end up with a majority?
first given data
| district/party | democratic | republic |
|---|---|---|
| 1 | 1 | 1 |
| 2 | 1 | 1 |
| 3 | 1 | 1 |
| 4 | 1 | 1 |
| 5 | 1 | 1 |
| 6 | 2 | 2 |
| 7 | 2 | 2 |
| 8 | 2 | 2 |
| 9 | 1 | 0 |
| 10 | 1 | 2 |
| 11 | 1 | 2 |
| 12 | 3 | 1 |
total unique outcomes, that is either republic or democratic party should win at each place
= 2C1*2C1*2C1*2C1*2C1*4C1*4C1*4C1*1C1*3C1*3C1*4C1
= 25*32*44
for a party to win it should get more than 6 wins the calculation of theese outcomes is most complex since member distribution is not unique. It needs excel to calculate this.
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