13. Two Indiana state candidates must decide which city to visit the day before the November election. The same four cities-Indianapolis, Evansville, Fort Wayne, and South Bend-are available for both candidates. These cities are listed as strategies 1 to 4 for each candidate. Travel plans must be made in advance, so the candidates must decide which city to visit prior to knowing the other candidate’s plans. Values in the following table show thousands of voters for the Republican candidate based on the strategies selected by the two candidates based on the strategies selected by the two candidates. Democrat Candidate Indianapolis Evansville Fort Wayne South Bend b1 b2 b3 b4Republican Candidate Indianapolis, a1 0 -15 -8 20 Evansville, a2 30 -5 5 -10 Fort Wayne, a3 10 -25 0 20 South Bend, a4 20 20 10 15a. What strategy should the Republican candidate take?b. What strategy should the Democrat candidate take?
Permutations and Combinations
If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.
Counting Theory
The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.
13. Two Indiana state candidates must decide which city to visit the day before the November election. The same four cities-Indianapolis, Evansville, Fort Wayne, and South Bend-are available for both candidates. These cities are listed as strategies 1 to 4 for each candidate. Travel plans must be made in advance, so the candidates must decide which city to visit prior to knowing the other candidate’s plans. Values in the following table show thousands of voters for the Republican candidate based on the strategies selected by the two candidates based on the strategies selected by the two candidates.
Democrat Candidate
Indianapolis Evansville Fort Wayne South Bend
b1 b2 b3 b4
Republican Candidate Indianapolis, a1 0 -15 -8 20
Evansville, a2 30 -5 5 -10
Fort Wayne, a3 10 -25 0 20
South Bend, a4 20 20 10 15
a. What strategy should the Republican candidate take?
b. What strategy should the Democrat candidate take?
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