There is a rumor that Daddy Warbucks is starting a new airline. He plans to serve six cities: San Francisco, Los Angeles, Dallas, Chicago, New York, and Miami. There will be direct flights between each pair of cities. How many different routes will this create?
Answer: There will be [tex]15(5+4+3+2+1+0=15)[/tex] different routes.
The 15 different routes are:
1. San Francisco ------------ Los Angeles
2. San Francisco ------------ Dallas
3. San Francisco ------------ Chicago
4. San Francisco ------------ New York
5. San Francisco ------------ Miami
6. Los Angeles ------------ Dallas
7. Los Angeles ------------ Chicago
8. Los Angeles ------------ New York
9. Los Angeles ------------ Miami
10. Dallas ------------ Chicago
11. Dallas ------------ New York
12. Dallas ------------ Miami
13. Chicago ------------ New York
14. Chicago ------------ Miami
15. New York ------------ Miami
Answer: 15
Step-by-step explanation:
The number of combinations of n things where r things taken at a time is given by :-
[tex]C(n;r)=\dfrac{n!}{( n-r)!r!}[/tex]
Given : Total number of places (San Francisco, Los Angeles, Dallas, Chicago, New York, and Miami.)= 6
Then , the number of possible pairs of any two city will be :-
[tex]C(6;2)=\dfrac{6!}{(6-2)!2!}\\\\=\dfrac{6\times5\times4!}{4!\times2}=15[/tex]
Hence, the number of different routes will this create = 15
