How many ways can one place $8$ pawns on a $4$x$4$ chess board such that each row and each column contains exactly $2$ pawns?
I figured a brute-force way where I go row by row placing $2$ pawns each and tracking the number of ways in which the column criteria are met.
Is there a more elegant (shorter or better structured) approach? What I mean is given we need to place $2n^2$ pawns in a $4n^2$ square board with each row column containing exactly $n$ pawns, this approach won't be scalable since I can't use the above result recursively either.