一道关于棋子摆放的小学数学竞赛题

函笑

Using 16 black pawns and 16 white pawns, how many ways can we place 16 pawns into the 4x4 chessboard, where each pawn is occupying 1 cell, such that in each row and in each column the number of white pawns is even?
用16个黑棋和16个白棋，在4×4的棋盘上，每个棋子占1格，使每行和每列的白棋数量为偶数，我们可以用多少种方法放置16个棋子？