 Solution

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/v/solution

Let

E_{5}

denote the set of arrangements with

E

fifth, and

F_{6}

those with

F

sixth. Each contains

5!

arrangements, while their intersection contains

4!

∣ E_{5} \cup F_{6} ∣ = 5! + 5! - 4! = 216 .

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