How to choose a city by random selection?

According to the meaning of the question, each of the five students randomly chooses a city from three different cities to travel.

Everyone has three choices, so five people have 35=243 choices.

If all three cities have candidate cities, it needs to be analyzed in two steps:

Firstly, divide five people into three groups.

If it is divided into three groups: 2, 2 and 1, there are five cases of C25C311a22 =1.

If it is divided into three groups: 3, 1 and 1, there are three situations: C35c12c11a22 =10.

* * * There are 15+ 10=25 grouping methods.

② Divide the three groups into three cities with A33=6 situations.

Then all three cities have candidates in the case of 25×6= 150.

So the probability that all three cities have candidates is150243 = 5081;

So the answer is: 508 1