A certain identification number is a sequence of eight digits.

(a) How many identification numbers are possible?

To calculate how many identification numbers are possible, we need to consider the total number of digits and the options for each digit.

(a) Since each identification number is a sequence of 8 digits, and each digit can be any number from 0 to 9, there are 10 possible choices for each digit (0, 1, 2, ..., 9). 

The total number of identification numbers is then calculated by multiplying the number of possibilities for each digit:

\[
10 \times 10 \times 10 \times 10 \times 10 \times 10 \times 10 \times 10 = 10^8
\]

Thus, the total number of possible identification numbers is:

\[
10^8 = 100,000,000
\]

### Answer:
There are **100,000,000** possible identification numbers.

Do you want more details on this, or have any further questions?

Here are 5 related questions to expand on this concept:
1. How many identification numbers are there if the sequence is 5 digits long?
2. What if the identification number cannot start with 0, how many numbers are possible then?
3. How many 8-digit identification numbers contain only even digits?
4. If the identification number must be a palindrome (same forwards and backwards), how many possible numbers are there?
5. How many 8-digit identification numbers are possible if no digit repeats?

**Tip:** When dealing with permutations and combinations, always check if repetitions are allowed for clarity.

A certain identification number is a sequence of eight digits.
(a) How many identification numbers are possible?

Explore the solution to the problem of finding how many 8-digit identification numbers are possible. Understand the key concepts of combinatorics, counting principles, and the multiplication principle of counting. Suitable for students in Grades 5-7.

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