Math Problem Statement
Solution
To solve this problem, we need to calculate how many possible passwords can be created with the given constraints.
Problem Breakdown:
- The password consists of two digits followed by two letters.
- 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 available letters.
- Digits: Normally, there are 10 digits (0–9). After removing 3 and 6, we have available digits.
Calculation:
- For the two digits: Since digits can repeat, there are 8 choices for each of the two digits.
- For the two letters: Since letters can repeat, there are 23 choices for each of the two letters.
Total Passwords:
To find the total number of passwords, we multiply the number of choices for the digits and letters:
Thus, 33,856 passwords can be created using this format.
Would you like more details or have any further questions?
Related Questions:
- What if the letters and digits could not be repeated?
- How would the total change if more digits were excluded?
- What if the password required three digits and three letters instead?
- How many passwords could be created if letters were case-sensitive?
- 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!
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Math Problem Analysis
Mathematical Concepts
Combinatorics
Multiplication Principle
Formulas
Total Passwords = (Available Digits)^2 * (Available Letters)^2
Theorems
Multiplication Rule of Counting
Suitable Grade Level
Grades 9-12
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