Five cities A, B, C, D and F are connected as shown below. ‘Train Ace’ provides

Question

Five cities A, B, C, D and F are connected as shown below. ‘Train Ace’ provides fast trips, connecting neighboring cities only. Tommy the traveler decides to consider the cost of buying tickets for all available arrangements of three different trips. For example A-B, A-C, C-A. The direction of the route matters. A-B and B-A are considered two different trips. Each one way ticket costs $20. Calculate the total cost in $ for someone who tries all available three-trip-packages.

A ------------- B ------------- C -------------- D ------------- F

Explanation / Answer

Clearly three trip pack consist of three cities or by taking three letters out of total 5 letters. So total ways of selecting 3 cities out of 5 cities be :

nCr=n!/(r! x (n-r)!)

or 5C3 = 5!/(3!(5-3)!)= (5 x 4 x 3!)/(2 x 3!) = (5 x 4)/2 = 10

But as order matters here, so these three cities can further be arranged in total 3! ways.

So total available three trip packages will be 10 x 6= 60 trips.

And as each three trip pack consists of three onw way ticket routes, that means one single three trip will have total =20 x 3 =$60 as total cost for that trip.

Thus total cost for all available three trip packages = $60 x 60 = $3600

Answer

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