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To solve this problem, we need to calculate how many possible passwords can be created with the given constraints.

### Problem Breakdown:
1. The password consists of **two digits** followed by **two letters**.
2. Certain letters (J, K, and L) and digits (3 and 6) are excluded.
   
### Available Options:
- **Letters**: Normally, there are 26 letters in the English alphabet. After removing J, K, and L, we have \( 26 - 3 = 23 \) available letters.
- **Digits**: Normally, there are 10 digits (0–9). After removing 3 and 6, we have \( 10 - 2 = 8 \) available digits.

### Calculation:
- For the **two digits**: Since digits can repeat, there are 8 choices for each of the two digits.
  \[
  8 \times 8 = 64 \text{ choices for the two digits}.
  \]
- For the **two letters**: Since letters can repeat, there are 23 choices for each of the two letters.
  \[
  23 \times 23 = 529 \text{ choices for the two letters}.
  \]

### Total Passwords:
To find the total number of passwords, we multiply the number of choices for the digits and letters:
\[
64 \times 529 = 33,856 \text{ possible passwords}.
\]

Thus, **33,856** passwords can be created using this format.

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Would you like more details or have any further questions?

### Related Questions:
1. What if the letters and digits could not be repeated?
2. How would the total change if more digits were excluded?
3. What if the password required three digits and three letters instead?
4. How many passwords could be created if letters were case-sensitive?
5. What would be the total number of passwords if only vowels could be used as letters?

**Tip:** When solving combinatorics problems, always check for restrictions and whether repetition is allowed!

Suppose a company needs temporary passwords for the trial of a new payroll software. Each password will have two digits followed by two letters. The letters J, K, and L and the digits 3 and 6 will not be used. So, there are 23 letters and 8 digits that will be used. Assume that the letters and digits can be repeated. How many passwords can be created using this format?

Find out how to calculate the number of possible passwords when certain letters and digits are excluded. This combinatorics problem involves the multiplication principle and applies the rule of counting to a real-world scenario. Suitable for students in Grades 9-12.

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