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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 first 3 letters of the alphabet and the first 5 digits?

Options:

  1. 150
  2. 180
  3. 120
  4. 100

Correct Answer: 180

Solution: 

The number of ways to choose 3 letters from 3 is 3! and 2 digits from 5 is 5P2. Total = 3! * 5P2 = 6 * 20 = 120.

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 first 3 letters of the alphabet and the first 5 digits?
  1. 150
  2. 180
  3. 120
  4. 100

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 first 3 letters of the alphabet and the first 5 digits?
  • Step 1: Identify the letters and digits available. We have the first 3 letters of the alphabet: A, B, C. We also have the first 5 digits: 0, 1, 2, 3, 4.
  • Step 2: Calculate the number of ways to arrange the 3 letters. Since we have 3 letters and we want to use all of them, we can arrange them in 3! (3 factorial) ways. 3! = 3 × 2 × 1 = 6.
  • Step 3: Calculate the number of ways to choose and arrange 2 digits from the 5 available digits. This is done using permutations since the order matters. The formula for permutations is 5P2, which is calculated as 5! / (5-2)! = 5 × 4 = 20.
  • Step 4: Multiply the number of arrangements of letters by the number of arrangements of digits to find the total number of different passwords. Total = 3! × 5P2 = 6 × 20 = 120.
  • Permutations and Combinations – The question tests the understanding of how to calculate the number of arrangements of letters and digits using permutations and combinations.
  • Factorials – The use of factorials to determine the number of ways to arrange the letters is a key concept in combinatorial mathematics.
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