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A new flag is to be designed with six vertical stripes using some or

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A new flag is to be designed with six vertical stripes using some or [#permalink]

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A new flag is to be designed with six vertical stripes using some or all of the colors yellow, green, blue and red. Then, the number of ways this can be done such that no two adjacent stripes have the same color is ?

(1) 12x81
(2) 16 x 192
(3) 20x 125
(4) 24x216
(5) None of the above
[Reveal] Spoiler: OA

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Last edited by Bunuel on 16 May 2017, 06:33, edited 1 time in total.
Renamed the topic and edited the question.
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Re: A new flag is to be designed with six vertical stripes using some or [#permalink]

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Kritesh wrote:
A new flag is to be designed with six vertical stripes using some or all of the colors yellow, green, blue and red. Then, the number of ways this can be done such that no two adjacent stripes have the same color is ?

(1) 12x81
(2) 16 x 192
(3) 20x 125
(4) 24x216
(5) None of the above


Hi

There are 6 stripes and 4 colors for them.

For the fist stripe we can use all 4 colors - no constrains.

For the second, however, we can't choose color already chosen for the first one, hence 4-1 = 3. For the third we can't choose color, chosen for the second, but can choose one used for the first - again 3. Same logic for the rest.

Final result: \(4*3*3*3*3*3 = 4*3^5 = 12*81\)

Answer A.
Re: A new flag is to be designed with six vertical stripes using some or   [#permalink] 16 May 2017, 06:58
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A new flag is to be designed with six vertical stripes using some or

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