We can solve this problem by using the principle of inclusion-exclusion to calculate how many students have visited any of the three countries (Germany, France, or Spain). Then, we subtract that from the total number of students (43) to find out how many haven't visited any of the countries.

Given Information:

• Total students: 43
• $G$ (Germany): 18 students
• $S$ (Spain): 22 students
• $F$ (France): 19 students
• $G \cap F$ (Germany and France): 10 students
• $G \cap S \cap F$ (Germany, France, and Spain): 3 students
• Only Germany: 2 students
• Only Spain: 8 students
• Only Spain and France: 5 students

Step 1: Calculate unique groups from the given data.

We know:

• Only Germany: 2 students.
• Only Spain: 8 students.
• Only Spain and France: 5 students.
• All three countries: 3 students.

Next, we need to calculate how many have visited Germany and France but not Spain, and Germany and Spain but not France.

Germany and France (but not Spain):

This is given as $G \cap F$, but we need to exclude those who visited all three countries. $(G \cap F) \text{ but not Spain} = 10 - 3 = 7.$

Germany and Spain (but not France):

To find this, we need to subtract those who visited all three countries from the total who visited both Germany and Spain. However, this information isn't directly given. But using inclusion-exclusion, we can later calculate this missing piece.

Step 2: Use the principle of inclusion-exclusion.

The formula for finding the number of people who visited at least one of the countries is: $|G \cup F \cup S| = |G| + |F| + |S| - |G \cap F| - |G \cap S| - |F \cap S| + |G \cap F \cap S|.$ We already have $|G| = 18$, $|F| = 19$, and $|S| = 22$, and $G \cap F = 10$, and $G \cap F \cap S = 3$.

To find $G \cap S$ and $F \cap S$, we need to figure out how many have been to Germany and Spain and France and Spain.