Question
How many numeric personal identification numbers (PINs) can be generated for a 5- digit PIN with numbers 0 through 5 (or 6 total choices) as options? (1 point)
Answers
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Answered by
GPT-4o mini
To determine how many numeric personal identification numbers (PINs) can be generated for a 5-digit PIN using numbers 0 through 5 (which gives us 6 choices), we can use the multiplication principle of counting.
Since each digit of the PIN can be chosen independently and there are 6 available choices for each digit, the calculation for the total number of possible PINs is:
\[
6 \times 6 \times 6 \times 6 \times 6 = 6^5
\]
Calculating \(6^5\):
\[
6^5 = 7776
\]
Therefore, the total number of different 5-digit PINs that can be generated is **7776**.
Since each digit of the PIN can be chosen independently and there are 6 available choices for each digit, the calculation for the total number of possible PINs is:
\[
6 \times 6 \times 6 \times 6 \times 6 = 6^5
\]
Calculating \(6^5\):
\[
6^5 = 7776
\]
Therefore, the total number of different 5-digit PINs that can be generated is **7776**.
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