In one variant of chess, known as Fischer chess, the initial positions of the pieces are determined by a random draw, adhering to the following rules:

- the light pieces must be on the a1, b1, ..., h1 squares;

- the king must be between the two rooks;

- the two bishops must be on squares of opposite colors;

- the dark pieces must be on the a8, b8, ..., h8 squares, in the same order as the light pieces. How many possible starting positions are there?
We can place the two runners on 4 positions each, which gives a total of $4 \cdot 4=16$ possibilities. After that, 6 positions remain for the queen and the two knights, which can be arranged in $\frac{6 \cdot 5 \cdot 4}{2}=60$ ways. Finally, for the remaining 3 squares, the king must go in the middle, and the two rooks must go on the two outer squares, which is only 1 possibility.

Thus, the total number of initial positions is $16 \cdot 60 \cdot 1=960$.