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A city has 12 districts. An election is coming up for the city metro council (1...

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?

Math   Statistics-And-Probability   
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Answer #1

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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