The number of matchings

Task number: 4179

How many matchings there exist on \( 2n \) vertices (for the sprinkler truck problem)?

  • Answer

    The number if matchings is just as many as partitions into pairs, that is \(\binom{2n}{2{,}2,…,2}\cdot\frac{1}{n!}=3{\cdot} 5 \cdot … \cdot (2n-1)\).

Difficulty level: Easy task (using definitions and simple reasoning)
Reasoning task
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