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A password consists of 3 letters followed by 2 digits. How many different passwo

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Question: A password consists of 3 letters followed by 2 digits. How many different passwords can be formed if letters can be repeated but digits cannot? (2000)

Options:

  1. 17576
  2. 15600
  3. 13000
  4. 12000

Correct Answer: 17576

Exam Year: 2000

Solution: 

There are 26 choices for each letter (3 letters) and 10 choices for the first digit and 9 for the second. Total = 26^3 * 10 * 9 = 17576.

A password consists of 3 letters followed by 2 digits. How many different passwo

Practice Questions

Q1
A password consists of 3 letters followed by 2 digits. How many different passwords can be formed if letters can be repeated but digits cannot? (2000)
  1. 17576
  2. 15600
  3. 13000
  4. 12000

Questions & Step-by-Step Solutions

A password consists of 3 letters followed by 2 digits. How many different passwords can be formed if letters can be repeated but digits cannot? (2000)
  • Step 1: Identify the components of the password. It consists of 3 letters followed by 2 digits.
  • Step 2: Determine how many choices there are for each letter. There are 26 letters in the English alphabet.
  • Step 3: Since letters can be repeated, for each of the 3 letters, you have 26 choices. So, for 3 letters, the total choices are 26 * 26 * 26, which is 26^3.
  • Step 4: Calculate 26^3. This equals 17576.
  • Step 5: Now, look at the digits. The first digit can be any of the 10 digits (0-9), so there are 10 choices for the first digit.
  • Step 6: For the second digit, since digits cannot be repeated, you have 9 choices left (one digit has already been used).
  • Step 7: Multiply the number of choices for the letters and the digits together. This gives you 26^3 (for letters) multiplied by 10 (for the first digit) multiplied by 9 (for the second digit).
  • Step 8: The final calculation is 17576 (from letters) * 10 (first digit) * 9 (second digit).
  • Step 9: Calculate the final total: 17576 * 10 * 9 = 1581840.
  • Combinatorics – The question tests the understanding of counting principles, specifically permutations and combinations, where repetition is allowed for letters but not for digits.
  • Permutations with Restrictions – It assesses the ability to apply different rules for different parts of a combination, such as allowing repetition in one part (letters) and not in another (digits).
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