Here's what I get
A) Assuming that the chairs of each color are identical
You have calculated the the number of possible arrangements correctly
If two white chairs are together they could occupy positions
1,2 and the other white chair can occupy positions 4,5,6,7 or 8
2,3 and the other white chair can occupy positions 5,6,7 or 8
3,4 and the other white chair can occupy positions 1, 6, 7 or 8
4,5 and the other white chair can occupy positions 1,2, 7 or 8
5,6 and the other white chair can occupy positions 1,2,3 or 8
6,7 and the othe white chair can occupy positions 1,2,3 or 4
7,8 and the other white chair can occupy positions 1,2,3,4,5
So.....we have 30 arrangements here
Three white chairs together can occupy any of 6 positions
So......the total number of excluded arragements = 36
So....the total number of acceptable arrangememts = 5040 - 36 = 5004
