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

Explanation:

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

`C(n;r)=(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)=(6!)/((6-2)!2!)\\\\=(6*5*4!)/(4!*2)=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