Problem Analysis:
We need to find the total number of ways to select a group of tickets such that the sum of their numbers is divisible by 5. Each ticket has a unique number from 1 to 200.

Solution:
To solve this problem, we can use the concept of modular arithmetic. Let's consider the following points:

1. Finding all possible remainders:
- We know that a number is divisible by 5 if and only if its remainder when divided by 5 is 0.
- Therefore, we need to find all the possible remainders when the ticket numbers are divided by 5.

2. Counting the number of tickets with each remainder:
- We need to count the number of tickets that leave a remainder of 0, 1, 2, 3, or 4 when divided by 5.
- To do this, we can iterate through all the ticket numbers from 1 to 200 and count the number of tickets that leave a specific remainder when divided by 5.

3. Forming groups with a sum divisible by 5:
- Once we have the count of tickets for each remainder, we can calculate the possible combinations of tickets that form a sum divisible by 5.
- To do this, we can consider all possible combinations of tickets from each remainder group and check if their sum is divisible by 5.
- We can use the concept of combinations to calculate the total number of ways to select tickets from each remainder group.

4. Calculating the total number of selections:
- Finally, we sum up the number of possible selections from each remainder group to get the total number of ways to select tickets whose sum is divisible by 5.

Implementation:
Here is the step-by-step implementation of the solution:

1. Initialize an array to store the count of tickets for each remainder (0 to 4).
2. Iterate through all the ticket numbers from 1 to 200.
- Calculate the remainder when the ticket number is divided by 5.
- Increment the count of tickets for that remainder.
3. Initialize a variable to store the total number of selections.
4. Iterate through each remainder group (0 to 4).
- Calculate the total number of ways to select tickets from that group using the concept of combinations.
- Add the count to the total number of selections.
5. Print the total number of selections.

Conclusion:
By following the above steps, we can calculate the total possible number of selections of tickets such that the sum of their numbers is divisible by 5.