<>What works well with the program is sticking the king and rooks where they usually belong >and randomize the other pieces. This gives 740 different setups.

How did you come up with that number? My calculations give 720.

The number of initial positions where the Rooks and the King is on their "normal" places AND the Bishops are on different colors is:

(7!/4) - (5!/2)·(6+3) = 1260 - 540 = 720


>If you randomize all the pieces except that bishops are on opposite colors and king between >rooks there are 84,000 different ways.

I agree on that. The number F we are looking is:

F = (Σ[{i=1,8} (i+1)·i/2])·(7!/4) - (5!/2)·9·((Σ[{k=1,8} (k+1)·k/2])-6·3-4·5-2·7) - 6·a-4·b-2·c

where:
a = 2·(5!/2)·(6+3) + (5!/2)·(10+1)
b = 3·(5!/2)·(6+3) + 2·(5!/2)·(10+1)
c = 4·(5!/2)*(6+3) + 3·(5!/2)·(10+1)

And it really results in 84000.

How did you calculated that number? You used the following method or something different? I hope you didn't count all positions by hand:-)