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Answer :
Final answer:
To find the number of 4-digit PINs with no repeated digits, calculate the product of the available options for each digit, which is 10 × 9 × 8 × 7, resulting in 5040 unique PINs.
Explanation:
The question asks us to determine how many different personal identification numbers are possible if each number consists of 4 digits, with no digit being repeated. Since we have 10 digits (0 through 9) to choose from for the first digit, there are 10 options. For the second digit, one digit has already been used, so there are 9 options remaining. This pattern continues with 8 options for the third digit and 7 options for the fourth digit. To find the total number of unique 4-digit PINs possible we must calculate the product of these options, which is 10 × 9 × 8 × 7.
Let's perform the calculation step by step:
- For the first digit: 10 possibilities (0-9)
- For the second digit: 9 possibilities (excluding the first chosen digit)
- For the third digit: 8 possibilities (excluding the first two chosen digits)
- For the fourth digit: 7 possibilities (excluding the first three chosen digits)
- Multiply the number of possibilities for each digit position: 10 × 9 × 8 × 7 = 5,040
The correct answer to how many different 4-digit PINs are possible if no digit is repeated is 5040, answer choice b.
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