I am not sure about this.
let 000=x
let 111=y
thus total digit positions now reduces to 4 ( x=000,y=111 ,and other bit positions can be 0 or 1)
now how do we arrange these 6 digits,
now
0 0 0 0 x y
0 0 0 0 y x
and so on
number of ways u can place x and y are
xx_ _ _ _
x_ x_ _ _
x_ _ x_ _.
x_ _ _ x_
x_ _ _ _ x
there are 5 ways where each of xx can be replaced by xx xy yx yy,thus 5*4=20 ways, similarly calculate with X starting from 2nd position
number of ways x,y can be filled are 20+16+12+4+8 = 60 ways
in each of 60 ways we can arrange remaining 4 bits in 16 ways
therefore number of ways is 60*16=960 ways, but here all 0's all 1's are repeated for all 59 times,
therefore total ways = 960-(59*2)=960-158= 802 ways
I am not at all sure about this method, just gave a try
