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

- no two adjacent flags are of the same colour.
- the flags at the two ends of the line are of different colours.

In how many different ways can the flags be arranged?

- 6
- 4
- 10
- 2

+1 vote

Best answer

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))**

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