A businesswoman in Philadelphia is preparing for a visit to six major cities. the distance traveled, and hence the cost of the trip, will depend on the order in which she plan her route.

a. How many different Itineraries (and the trip costs) are possible?
b. if the businesswoman randomly selects one of the possible itineraries and Denver and San Francisco are two of the cities she plans to visit, what is the probability that she will visit Denver before San Francisco?

Question

A businesswoman in Philadelphia is preparing for a visit to six major cities. the distance traveled, and hence the cost of the trip, will depend on the order in which she plan her route.

a. How many different Itineraries (and the trip costs) are possible?
b. if the businesswoman randomly selects one of the possible itineraries and Denver and San Francisco are two of the cities she plans to visit, what is the probability that she will visit Denver before San Francisco?

anonymous · Answer

There are 6factorial ways to order the 6 cities. Maybe you can list them all out and then see how many of those have Denver before SF. Is this method allowed?

anonymous · Answer

I know answer for part b is 1/2 by simply doing an experiment on a smaller scale but I don't understand how can one use counting method (mn rule, combination, and permutation) to come up with the answer?

anonymous · Answer

Would the answer be very complicated then because we have to consider the scenarios when Denver is visited first thru fifth?