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DotKite
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Homework Statement
A businesswoman in Philadelphia is preparing an itinerary 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 plans the route.
a) how many different itineraries ( and trip costs) are possible)?
Since order is significant I used the equation for permutations and arrived at an answer of 720 possible itineraries. (I hope this much is correct)
b) If the business woman selects one of the possible itineraries and Denver and San Francisco are two of the cities she plans to visit, what is the probability she will visit Denver before San Francisco?
Homework Equations
The Attempt at a Solution
OK I am just terrible at this stuff. I never know how to count anything. I go over and over on the principles of counting, but I fail to be able to apply them. part a I understand. It is 6!. However part b just immediately confuses me.
So you want all possibilities that denver is before san fran.
D F _ _ _ _
_ D F _ _ _
_ _D F _ _
_ _ _ D F _
_ _ _ _ D F
For each of these "possibilities" there are still 4 cities to be ordered. So for each of those listed there are 4! different ways to arrange each one of them? here is where i get stuck