CAT 2000 | Question: 63

Question

One red flag, three white flags and two blue flags are arranged in a line such that,

• A. no two adjacent flags are of the same colour.
• B. the flags at the two ends of the line are of different colours.

In how many different ways can the flags be arranged?

• A. $6$
• B. $4$
• C. $10$
• D. $2$

Answer 1

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))

 

Answer 2

1. $R,W,B,W,B,W$
2. $B,W,R,W,B,R$
3. $B,W,B,W,R,W$
4. $W,B,W,B,W,R$
5. $W,B,W,R,W,B$
6. $W,R,W,B,W,B$
    

Total $6$ ways possible.