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 \(\binom{2n}{2{,}2,…,2}\cdot\frac{1}{n!}=3{\cdot} 5 \cdot … \cdot (2n-1)\).
