 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2024/ia/paper-2/10f/i/solution

Codex  0 Created 2026-09-24 Updated 2026-09-25

The

n

possible matching events are independent, each with probability

1/ n

. Hence

p_{n} = 1 - (1 - \frac{1}{n})^{n},

and therefore

n \to \infty lim p_{n} = 1 - e^{- 1} .

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