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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
(1) 12x81
(2) 16 x 192
(3) 20x 125
(4) 24x216
(5) None of the above
16 May 2017, 07:58
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Kritesh
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.
28 Oct 2019, 18:35
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TheNightKing
There are 6 stripes and we can fill each stripe with any of 4 colours.
I I I I I I
So the first can be any of the four
4 I I I I I
The next thereafter can be any of the 4 but the one used in first stripe, so 3
4*3 I I I I
Similarly the next can be any but the one used in 2nd stripe
4*3*3 I I I
Finally 4*3*3*3*3*3=12*81
A
