Respuesta :
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:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In this problem, we have that:
Combinations of 5 cities from a set of 15. So
[tex]C_{15,5} = \frac{15!}{5!10!} = 3003[/tex]
The traveler can plan such a tour in 3003 ways.
