Q1. 1 red flag, 3 white flags and 2 blue flags are arranged in a line
such that:
I. No two adjacent flags are of the same colour
II. The flags at the ends are of 2 different colours.
In how many different ways the flags be arranged?

• Case 1:
  
  W_W_W_
  
  Case 2:
  
  _W_W_W
  
  
  we have 3 slots free where we have to arrange 3 flags.
  3 flags can be arranged in 3! ways.
  out of 3 flags, two are blue (identical).
  Taking care of the 2 indistinguishable choices, we get, 3!/2! ways per case.
  
  Since there are 2 cases, we get 2*3!/2!
• 6 years agoHelpfull: Yes(14) No(3)
• 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
• 5 years agoHelpfull: Yes(4) No(1)
• Answer is 36.. Because No two adjacent flags are of the same color..so assume 1 arrangement as B W B W R W.. so to arrange 2 blue balls,ways are 2!.. to arrange 3 white balls,ways are 3!.. & to arrange 1 red ball,ways are 1!.. & also , we are not confirm about which ball should come first, so again there are 3 ways. So,total = 2!*3!*1! * 3 = 36
• 6 years agoHelpfull: Yes(2) No(7)
• WBWBWR
  WBWRWB
  WRWBWB
  BWBWRW
  BWRWBW
  RWBWBW
  WBRWBW
  WRBWBW
  WBWBRW
  WBWRBW
  10 WAYS
• 5 years agoHelpfull: Yes(1) No(6)
• 6 ways is the answer
• 5 years agoHelpfull: Yes(1) No(2)