Traveling Salesperson Suppose you are a salesperson who must visit the following 23 cities: Dallas, Tampa, Orlando, Fairbanks, Seattle, Detroit, Chicago, Houston, Arlington, Grand Rapids, Urbana, San Diego, Aspen, Little Rock, Tuscaloosa, Honolulu, New York, Ithaca, Charlottesville, Lynchville, Raleigh, Anchorage, and Los Angeles. Leave all your answers in factorial form.

a. How many possible itineraries are there that visit each city exactly once?

b. Repeat part (a) in the event that the first five stops have already been determined.

c. Repeat part (a) in the event that your itinerary must include the sequence Anchorage, Fairbanks, Seattle, Chicago, and Detroit, in that order.

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ogorwyne ogorwyne · Answer 1 · 2021-02-19T20:02:07+01:00

Answer:

1. 23!

2. 18!

3. 19!

Step-by-step explanation:

1.

We start by the order that we were given. Dallas is the first City with los Angeles being the last.. a total of 23 states.

Dallas can be placed in any of the 23 positions.

Tampa can be placed in any of the remaining 22 positions and so on.

Such that we have

Total number of ways = 23x22x21...x1 ways

= 23!

2. If first 5 cities have been determined,

23-5 = 18 cities

We can arrange in (23-5)! Ways

= 18!

3. We consider these 5 cities to be 1 unit, so we have to arrange the remaining 18 cities plus this single unit.

Total number of ways = (18+1)!

= 19!