3x3 grid of 1 to 9 with all lines even

The integers $1,2,\dots,9$ are each written once into the cells of a $3\times3$ grid. In how many arrangements do all three rows and all three columns have an even sum?

$0$ ways — it is impossible. Three numbers have an even sum exactly when an even number of them (0 or 2) are odd. So each row would contain an even count of odd numbers, making the total number of odd entries even, but $1,\dots,9$ contains five odd numbers. (The row condition alone already fails.)