The problem is about forming an 8-digit phone number using digits 0 through 9, under certain conditions. Let's break down and solve each part:

Problem Analysis:

1. The phone number must be 8 digits long.
2. The first digit cannot be 0 (it should be 1 to 9).

Solutions:

Let's calculate the number of phone numbers under each scenario:

a. Angka-angka boleh berulang (Digits can repeat)

• For the first digit, we have 9 options (1-9).
• For each of the remaining 7 digits, all 10 digits (0-9) can be used.

Thus, the number of phone numbers is: $9 \times 10^7 = 90,000,000$

b. Tidak boleh ada angka yang diulang (No digit repetition)

• For the first digit, we have 9 options (1-9).
• For the second digit, we have 9 options (0-9, excluding the first digit).
• For the third digit, 8 options remain, and so on.

So, the number of phone numbers is: $9 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 = 9 \times 9! / (9 - 7)!$ Calculating: $9 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 = 9 \times 181,440 = 1,632,960$

c. Hanya angka pertama yang tidak boleh diulang (Only the first digit cannot repeat)

• For the first digit, we have 9 options (1-9).
• For each of the remaining 7 digits, any of the 10 digits can be used, including the first digit.

Thus, the number of phone numbers is: $9 \times 10^7 = 90,000,000$

Summary:

• (a): 90,000,000 phone numbers
• (b): 1,632,960 phone numbers
• (c): 90,000,000 phone numbers

Would you like more details on any of these solutions or have any specific questions? Here are 5 related questions for further exploration:

1. How would the calculation change if the phone number length were increased to 9 digits?
2. What would happen if the first digit also allowed 0?
3. Can we derive a general formula for cases with varying digit restrictions?
4. What is the probability of selecting a number without repetition if chosen randomly?
5. How many unique phone numbers can be generated if only certain digits are allowed?

Tip: When counting possibilities, always account for restrictions first (e.g., "no repetition") before applying combinatorics.