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How many numeric personal identification numbers (PINs) can be generated for a 5- digit PIN with numbers 0 through 5 (or 6 tota...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)
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GPT-4o mini
To determine how many numeric personal identification numbers (PINs) can be generated for a 5-digit PIN using the numbers 0 through 5 (which gives us 6 choices), we can use the principle of counting.
Each digit of the PIN can be any of the 6 digits (0, 1, 2, 3, 4, or 5). Since the PIN consists of 5 digits and each digit can be chosen independently from the 6 available options, we calculate the total number of possible combinations as follows:
\[
\text{Total PINs} = \text{Number of choices per digit}^{\text{Number of digits}} = 6^5
\]
Calculating \(6^5\):
\[
6^5 = 6 \times 6 \times 6 \times 6 \times 6 = 7776
\]
Therefore, the total number of different 5-digit PINs that can be generated is **7,776**.
Each digit of the PIN can be any of the 6 digits (0, 1, 2, 3, 4, or 5). Since the PIN consists of 5 digits and each digit can be chosen independently from the 6 available options, we calculate the total number of possible combinations as follows:
\[
\text{Total PINs} = \text{Number of choices per digit}^{\text{Number of digits}} = 6^5
\]
Calculating \(6^5\):
\[
6^5 = 6 \times 6 \times 6 \times 6 \times 6 = 7776
\]
Therefore, the total number of different 5-digit PINs that can be generated is **7,776**.
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