Permutation and Combination doubt

Answer: 4!

Why is the answer not (6P3)/(2 * 2 * 2)?

There can be two ways to form flag

  1. Two same colour and one different
    3C2 x 2C1 x 3!/2! = 18

  2. All three different colour
    3C3 x 3! = 6

Ans- 18+6 = 24 = 4!

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Thank you.

I actually understood this but what I didn’t understand was why (6P3)/(2! * 2! * 2!) is wrong.

What flag combinations are not being included in (6P3)(2 * 2 * 2)?

I don’t really understand why you did 6P3… we don’t know which 3 strips will get selected out of 6… maybe same colour or all different and then you divide by 2, 3 times its means you are making flag of 6 strips

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It looks like I mixed up this question with questions about permutation of identical objects (like finding the number of words you can form from MISSISSIPPI which is 11!/(3! * 4! * 2!).

Thank you