# 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?

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Expert Answers

poetrymfa | 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`

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