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).

Answer 1

Answer:

The traveler can plan such a tour in 3003 ways.

Step-by-step explanation:

The order that the cities are chosen is not important, since it is chosen by the company and not by the traveler. So we use the combinations formula to solve this question.

Combinations formula:

$C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

In this problem, we have that:

Combinations of 5 cities from a set of 15. So

$C_{15,5} = \frac{15!}{5!10!} = 3003$

The traveler can plan such a tour in 3003 ways.