Question

The price of a European tour includes stopovers at five cities to be selected from 15 cities. In how many ways can a traveler plan such a tour if the traveler can only choose the five cities (the order is determined by the travel company).

A. 3,003

B. 15

C. 3

D. 360,360

E. 759,375

F. 75

Answer 1

The correct answer is D. 360,360.

Explanation:

Number of cities as stopovers available for selection for an European tour = 15

A traveler has to select a total of five cities from these the given 15 cities for his tour and order is determined by the travel company.

Therefore the number of ways the traveler plan such a tour is given by
`\left[\begin{array}{ccc}15\\5\end{array}\right]` = 3003.

Now the order of the cities chosen by the travel company is given by 3003 × 5! = 360,360 ways.