5 students each randomly choose a city to travel from 3 different cities, then the probability that all 3 cities are selected is ______

According to the meaning of the question, each of the 5 students randomly chooses a city to travel from 3 different cities.

Each person has 3 choices, so the 5 students have a maximum of 35 =243 selection situations,

If there are candidates in 3 cities, it needs to be analyzed in 2 steps:

①. First divide the 5 people into 3 groups,

If divided into three groups of 2, 2, and 1, there are 15 situations where C25C23C11A22=15,

If divided into three groups of 3,1,1, there are 10 situations where C35C12C11A22=10,

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

②. The three divided groups correspond to 3 cities, and there are A33=6 situations,

Then there are 25×6=150 situations where there are candidates in all three cities.

So the probability of candidates in all three cities is 150243=5081;

So the answer is :5081．