How many different 4-digit PIN codes can be formed using the digits 0-9 if digits cannot be repeated?

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Q: How many different 4-digit PIN codes can be formed using the digits 0-9 if digits cannot be repeated?

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

Steps: 9

Step 1: Understand that a 4-digit PIN code consists of 4 digits.
Step 2: Know that the digits can be any number from 0 to 9, which gives us a total of 10 digits.
Step 3: Since digits cannot be repeated, the first digit can be any of the 10 digits.
Step 4: After choosing the first digit, there are 9 digits left for the second digit.
Step 5: After choosing the first and second digits, there are 8 digits left for the third digit.
Step 6: After choosing the first three digits, there are 7 digits left for the fourth digit.
Step 7: Multiply the number of choices for each digit: 10 (first) * 9 (second) * 8 (third) * 7 (fourth).
Step 8: Calculate the total: 10 * 9 * 8 * 7 = 5040.
Step 9: Conclude that there are 5040 different 4-digit PIN codes possible.