How many different 4-digit PIN codes can be formed using the digits 0-9 without repetition?

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Q: How many different 4-digit PIN codes can be formed using the digits 0-9 without repetition?

Solution: The number of different 4-digit PIN codes is P(10, 4) = 10! / (10-4)! = 5040.

Steps: 10

Step 1: Understand that a 4-digit PIN code consists of 4 digits.
Step 2: Recognize that the digits can be any number from 0 to 9, which gives us a total of 10 possible digits.
Step 3: Since we cannot repeat any digits in the PIN code, we need to choose 4 different digits from the 10 available.
Step 4: For the first digit of the PIN code, we have 10 options (0-9).
Step 5: For the second digit, we can only choose from the remaining 9 digits (since one digit has already been used).
Step 6: For the third digit, we can choose from the remaining 8 digits.
Step 7: For the fourth digit, we can choose from the remaining 7 digits.
Step 8: To find the total number of different PIN codes, multiply the number of choices for each digit: 10 * 9 * 8 * 7.
Step 9: Calculate the result: 10 * 9 = 90, then 90 * 8 = 720, and finally 720 * 7 = 5040.
Step 10: Therefore, the total number of different 4-digit PIN codes that can be formed is 5040.