Question

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 1

Answer:  15

Step-by-step explanation:

The number of combinations of n things where r things taken at a time is given by :-

$C(n;r)=\dfrac{n!}{( n-r)!r!}$

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 :-

$C(6;2)=\dfrac{6!}{(6-2)!2!}\\\\=\dfrac{6\times5\times4!}{4!\times2}=15$

Hence, the number of different routes will this create = 15

Answer 2

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 $15(5+4+3+2+1+0=15)$ 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