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How many different 4-digit PINs can be formed using the digits 0-9 if digits can

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Question: How many different 4-digit PINs can be formed using the digits 0-9 if digits cannot be repeated?

Options:

  1. 5040
  2. 10000
  3. 9000
  4. 7200

Correct Answer: 5040

Solution: 

The first digit can be any of 10 digits, the second can be any of 9, the third can be any of 8, and the fourth can be any of 7. Total = 10 * 9 * 8 * 7 = 5040.

How many different 4-digit PINs can be formed using the digits 0-9 if digits can

Practice Questions

Q1
How many different 4-digit PINs can be formed using the digits 0-9 if digits cannot be repeated?
  1. 5040
  2. 10000
  3. 9000
  4. 7200

Questions & Step-by-Step Solutions

How many different 4-digit PINs can be formed using the digits 0-9 if digits cannot be repeated?
  • Step 1: Understand that a 4-digit PIN consists of 4 positions, and each position can be filled with a digit from 0 to 9.
  • Step 2: For the first digit, you can choose any of the 10 digits (0-9). So, there are 10 options for the first digit.
  • Step 3: For the second digit, you cannot use the digit you chose for the first digit. This leaves you with 9 remaining options.
  • Step 4: For the third digit, you cannot use the first or second digit. This leaves you with 8 options.
  • Step 5: For the fourth digit, you cannot use the first, second, or third digit. This leaves you with 7 options.
  • Step 6: To find the total number of different 4-digit PINs, multiply the number of options for each digit together: 10 (first) * 9 (second) * 8 (third) * 7 (fourth).
  • Step 7: Calculate the total: 10 * 9 * 8 * 7 = 5040.
  • Permutations – The question tests the understanding of permutations where the order matters and repetition is not allowed.
  • Counting Principles – It assesses the ability to apply the fundamental counting principle to determine the total number of combinations.
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