Question 5

Explanation

To arrange a card number consisting of $12$ digits, we need to understand the structure of the number.

Given:

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

The number of digits to be arranged is:

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

Since there is no rule prohibiting the repetition of digits in a phone number, each of the $4$ 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 $2401$.