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If a password consists of 3 letters followed by 2 digits, how many different pas

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Question: If a password consists of 3 letters followed by 2 digits, how many different passwords can be formed using the English alphabet and digits?

Options:

  1. 17576000
  2. 456976
  3. 100000
  4. 1000

Correct Answer: 17576000

Solution: 

There are 26 letters and 10 digits. The total combinations are 26^3 * 10^2 = 17576000.

If a password consists of 3 letters followed by 2 digits, how many different pas

Practice Questions

Q1
If a password consists of 3 letters followed by 2 digits, how many different passwords can be formed using the English alphabet and digits?
  1. 17576000
  2. 456976
  3. 100000
  4. 1000

Questions & Step-by-Step Solutions

If a password consists of 3 letters followed by 2 digits, how many different passwords can be formed using the English alphabet and digits?
  • Step 1: Identify the number of letters in the English alphabet. There are 26 letters.
  • Step 2: Identify the number of digits available. There are 10 digits (0-9).
  • Step 3: Determine how many letters are needed for the password. The password requires 3 letters.
  • Step 4: Calculate the number of combinations for the letters. Since each letter can be any of the 26 letters, the total combinations for 3 letters is 26 * 26 * 26, which is 26^3.
  • Step 5: Determine how many digits are needed for the password. The password requires 2 digits.
  • Step 6: Calculate the number of combinations for the digits. Since each digit can be any of the 10 digits, the total combinations for 2 digits is 10 * 10, which is 10^2.
  • Step 7: Combine the combinations of letters and digits. The total number of different passwords is the product of the combinations of letters and digits: 26^3 * 10^2.
  • Step 8: Calculate the final result. 26^3 equals 17576 and 10^2 equals 100, so 17576 * 100 equals 1757600.
  • Combinatorial Counting – The question tests the ability to calculate the total number of combinations of letters and digits in a specified format.
  • Permutations and Combinations – Understanding how to apply the rules of permutations and combinations to form passwords.
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