## Differential Equations and Linear Algebra (4th Edition)

$15$, odd
The ordered pairs that are out of order are: $(6,5),(6,4),(6,3),(6,2),(6,1),(5,4),(5,3),(5,2),(5,1),(4,3),(4,2),(4,1),(3,2),(3,1),(2,1)$, thus the number of inversions is $15$ and the parity is odd.