Since the balls are to be arranged in a row so that the adjacent balls are of different colours, therefore we can begin with a white ball or a black ball. If we begin with a white ball, we find that white balls numbered 1 to can be arranged in a row in ways. Now places are created between white balls which can be filled by black balls in ways.

So the total number of arrangements in which adjacent balls are of different colours and first ball is a white ball is . But we can begin with a black ball also. Hence the required number of arrangements is .