For each vertex, you need to find a pair. Lets select any one vertex. For this vertex, you can choose other pair vertex in (n-1)C1 ways. Similarly, we do for other vertices. So,
Ans = (n-1)C1 * (n-3)C1 * (n-5)C1 * ........ * (1)C1
Yeah but what exactly is this (n-1) different perfect colouring thing? I read it at wikipedia:
https://en.wikipedia.org/wiki/Edge_coloring#/media/File:Complete-edge-coloring.svg
Can you provide some insights?
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