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

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Official Explanation

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The other approach is to think in terms of White: If there are 3 whites and they are never together - then out of 6, they will either take all odd places or all even places.

White in odd places: The other 3 remaining place will be taken by 1 Red and 2 Blue. So an arrangement of 3 with 2 things similar:

\frac{3!}{2!}

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What this question tests

What it tests

Whether you can count arrangements and selections correctly — permutations vs. combinations.

Common trap

Overcounting: treating a selection as ordered when order does not matter, or forgetting to divide by duplicates.