Subjects combinatorics

Password Count

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Password Count


1. The problem asks for the total number of 4-digit passwords where each digit can be from 0 to 9 inclusive. 2. Since each digit can be any of 10 possible values (0 through 9), and there are 4 digits, the total number of passwords is calculated by multiplying the number of choices for each digit. 3. This is a case of counting with replacement, so the total number of passwords is: $$10 \times 10 \times 10 \times 10 = 10^4$$ 4. Calculate the value: $$10^4 = 10000$$ 5. Therefore, Jess can create a total of 10000 different 4-digit passwords.