A tourist in France wants to visit 5 different cities. If the route is randomly selected, what is the probability that she will visit the cities in alphabetical order?

Expert Answers
poetrymfa eNotes educator| Certified Educator

In order to answer this question, let's take a look at the reasoning behind it! There are many different kinds of probability problems, but this one relates to the Factorial Rule, which is:

n! = n x (n-1)!

In other words, "the factorial of any number is that number times the factorial of (1 smaller than that number)." 

So, if a tourist in France is visiting five different cities, and we want to know the probability that she will visit the cities in alphabetical order:

5! = 5 x 4 x 3 x 2 x 1 = 120

In other words, there are 120 different routes she could take. Since there is only one way to do this visit in alphabetical order, the probability will, thus, be:

`1/120`