Red flags are represented by R
White flags are represented by W
Blue flags are represented by B
And vacant spaces are represented by _
As No 2 adjacent flags are of the same colour, these are the 2 possible arrangements-
1. W_W_W_
OR
2. _W_W_W
Now, 1 red flag and 2 blue flags have to be arranged in these vacant places.
Hence, these 3 flags can be arranged in 3!/2! ways = 3 ways { RBB, BRB, BBR}
If we consider the 1st possible arrangement, then also these 3 flags can be arranged in 3 ways and this is applicable to the 2nd possible arrangement also.
So, Total number of ways = 3 + 3 ways
= 6 ways. (option 1))