Question

Suppose that you have been hired by the Gallup Organization, and your rst assignment is
to conduct a survey in each of the following state capitals: St. Paul (Minnesota), Sacramento (California),
Denver (Colorado), Jackson (Mississippi). As you plan your route of travel, you want to determine the
number of possible routes. How many di erent routes are possible?

Answer 1

4 Cities( St. Paul (Minnesota), Sacramento (California),Denver (Colorado), Jackson (Mississippi) to travel

Number of different possible routes = 4! = 4x3x2x1 = 24

a:St. Paul (Minnesota)

b: Sacramento (California)

c: Denver (Colorado)

d:Jackson (Mississippi)

Possible routes:

abcd, abdc, acbd, acdb,adbc,adcb - 6 routes

When first city is a:St. Paul (Minnesota) we have 6 routes

Similarly when first city is b: Sacramento (California) another 6 routes similarly 6 routes when c: Denver (Colorado) is the first city and another 6 routes when d:Jackson (Mississippi) is the first city

Therefore number of possible routes = 6 x 4 = 24