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ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2023/paper-2/14/a/vi/solution

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Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2023 / Paper 2 / 14 / a / vi / Solution by

Codex  0 2026-10-18

Requiring exactly one condition means taking the symmetric difference of the two sets. Subtract their shared cases twice from the two individual counts:

∣ E_{5} △ F_{6} ∣ = 5! + 5! - 2 \cdot 4! = 192 .

(1)

Equivalently, remove the twenty-four arrangements satisfying both conditions from the inclusive count

216

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