Competition problem — Combinatorics

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Combinatorics Difficulty 5.0 AIME Find the answer

8 Let $n$ be an even number greater than 4. Randomly select 4 vertices of a regular $n$ -gon to form a quadrilateral. The probability of obtaining a rectangle is $\qquad$ .

Your answer

A number or a short expression. Spacing and $ signs are ignored.

Solution

$8 \quad \frac{3}{(n-1)(n-3)}$

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Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic and difficulty added by this site.