Problem:
We need to find the total number of 5-digit numbers that can be formed using the digits 0, 1, 2, 3, 4, 7, and 8 without repetition, where each number is divisible by 9.

Solution:
To solve this problem, we can follow these steps:

Step 1: Identify the divisibility rule for 9:
A number is divisible by 9 if the sum of its digits is divisible by 9. So, we need to find the numbers that have a digit sum of 9.

Step 2: Determine the number of choices for each digit:
Since we want to form 5-digit numbers, we need to determine the number of choices we have for each digit. We can do this by counting the number of available digits for each position.

For the first digit, we have 7 choices (0, 1, 2, 3, 4, 7, 8).
For the second digit, we have 6 choices (any digit except the one already chosen).
For the third digit, we have 5 choices.
For the fourth digit, we have 4 choices.
For the fifth digit, we have 3 choices.

Therefore, the total number of choices for all five digits is 7 x 6 x 5 x 4 x 3 = 5040.

Step 3: Determine the number of valid combinations:
We need to find the number of combinations that have a digit sum of 9. To do this, we can use the concept of combinations.

Since the digits cannot be repeated, we need to find the number of combinations of 5 digits taken from the available choices (7 digits).

The formula for combinations is nCr = n! / (r!(n-r)!), where n is the total number of options and r is the number of choices.

Using this formula, we can calculate the number of combinations:

7C5 = 7! / (5!(7-5)!) = 7! / (5!2!) = (7 x 6 x 5 x 4 x 3 x 2 x 1) / ((5 x 4 x 3 x 2 x 1) x (2 x 1)) = 7 x 6 / 2 = 42.

So, there are 42 valid combinations.

Step 4: Determine the total number of valid numbers:
Now that we have the number of valid combinations, we need to find the total number of valid numbers. Since we have 5 digits, the number of valid numbers is equal to the number of valid combinations multiplied by the number of choices for each digit.

Total number of valid numbers = 42 x 5040 = 211,680.

Therefore, the correct answer is option A) 216.