Question 186525This question is from textbook
: Assume you started your own airline company called Safety Air (motto: “Your probability of a safe flight can never be greater than one.”), and you have one plane for a route connecting Savannah (GA), Birmingham (AL), New Orleans (LA), Tulsa (OK), El Paso (TX), Portland (OR), Rapid City (SD) and Omaha (NE). Every city must be serviced every day but will be serviced only once each day. How many other routes are possible if you must begin New Orleans and end in El Paso and do not revisit any airport?
This question is from textbook
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
There are eight cities listed, but one of them is fixed as the starting point and another is fixed as an ending point. So, there are six cities left for you to choose as the ending point of the first leg. Once you have chosen that city, there are five remaining to choose from, then four and so on. So, the theoretically possible number of routes is:
I say theoretically possible because, from a practical point of view, only a fraction of those 720 routes are really possible. For example, one of the most inefficient routes would be LA - GA - OR - AL - SD - OK - NE - TX (and then back to LA to be ready for the next day) is a little over 9000 miles, or 15 hours of flight time presuming you can average 600 mph ground speed. Figuring 2 hours per stop (and that is an agressive schedule) to get gas, discharge and board passengers, unload and load luggage, etc, for an additional 14 hours and you have 29 hours; more than a day.
John
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