The Question :
A tourist in France wants to visit 12 different cities. If the route is randomly selected, what is the probability that she will visit the cities in alphabetical order?
I thought about this in two ways and I got two different answers, both of them look correct to me ! but only one is correct.
1/144 (12 cities times 12 times to make the arrangement)
1/479001600 (which is generated by the permutation 12 P 12)
Which one is correct? and is there a better answer?
Please explain how do you know if the problem is permutation or combination or just simple multiplication.