# Thread: Inversions of a permutation

1. ## Inversions of a permutation

How can I show that the number of inversions of a permutaion of $\{1, 2, \dots , n\}$ is $n(n-1)/2$

2. Originally Posted by hcir614
How can I show that the number of inversions of a permutaion of $\{1, 2, \dots , n\}$ is $n(n-1)/2$
I guess by inversion you mean transpositions i.e. $2$-cycles. Note that any inversion has form $(ij)$ where $i and furthermore this is unique. Therefore the number of such inversions is ${n\choose 2} = \frac{n(n-1)}{2}$.