Question 8

Explanation

We need to determine how many card number combinations can be made based on the given rules.

The card number consists of $12$ digits with the following format:

1. First 4 digits (Prefix): Fixed, which is $0844$.
2. Last 4 digits (Suffix): Fixed, which is $1221$.
3. Middle 4 digits: The part that needs to be arranged.

Since the first 4 and last 4 digits are already determined, we only need to fill the $12 - 4 - 4 = 4$ empty positions in the middle.

The available digits to fill these positions are $\{2, 3, 4, 5, 7, 8, 9\}$. The number of available digit choices is $7$.

Since there is no restriction on repeating digits in arranging phone numbers, each of the 4 middle positions can be filled by any of the $7$ available digits.

The calculation is as follows:

Thus, the number of card numbers that can be created is $2401$.