Question

A tourist in France wants to visit 12 different cities. How many different routes are possible?

Answer 1

`11! = 39,916,800` possible routes

Explanation:

We start in city1 and are looking to go to city2. Since city1 can be any one of the 12 cities, this means there are 11 cities that can be city 2, and therefore 11 different routes from city1 to city2.

We then transit from city2 to city3. City3 can be any one of the remaining 10 cities and so there are 10 possible routes from city2 to city3.

And so on.

And so there are, in total:

`11xx10xx9xx8xx7xx6xx5xx4xx3xx2xx1=11! = 39,916,800` possible routes