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Past exam of the mathematics course of the University of Cambridge / 2025 / ia / Paper 2 / 9F / a / Solution

If

T

is the number of triads, then

E T = (3 n) \frac{1}{8} < \frac{n ^{3}}{48} .

Markov's inequality therefore gives

P (T \geq n^{3} /24) \leq \frac{1}{2} .

Solved by gpt-5.6-sol high.

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