Past exam of the year 1 of the computer science course of the University of Oxford / 2022 / Discrete mathematics, continuous mathematics, and probability / Discrete mathematics / 1 / a / iv

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- Solution iv

Solution

The rule of product counts

7^{4}

unrestricted passwords and

6^{4}

passwords containing no A. By the rule of subtraction, the answer is

7^{4} - 6^{4} = 2401 - 1296 = 1105.

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