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 / i

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- Solution i

Solution

For pairwise disjoint finite sets, the rule of sum gives

∣ ⋃_{i = 1}^{n} A_{i} ∣ = \sum_{i = 1}^{n} ∣ A_{i} ∣.

The password sets of different lengths are disjoint, so the required number is $P_{4} + P_{6} + P_{8}$ .

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