In how many ways is it possible to choose a white square and a black square on a

Total white squares = 32, total black squares = 32. For a given white square, black squares in the same row = 4, in the same column = 4 (disjoint), so valid black squares = 32 - 8 = 24. Total ways = 32 * 24 = 768. Alternatively, total pairs = 32*32 = 1024, subtract pairs sharing row (8 rows * 4*4 = 128) and sharing column (128) to get 1024 - 256 = 768.