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An advertising board is to be designed with 5 vertical stripes using some or all of colors red, yellow and orange. In how many ways board can be designed such that no two adjacent stripes have same color?

a)6

b)15

c)18

d)48
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48 should be the correct answer.
Let #@@@@ be the board where # denotes the leftmost strip and @'s denote remaining 4 strips.
We do not have to check for both left & right neighbour of each strip for boundary condition, but it would be enough to just check either left neighbour of each strip or right neighbour of each strip.
Here I am ensuring that none of the strip can have the same colour as its left neighbour.
Now since strip # has no left neighbour so it can have any of the 3 colours.
Remaining four strips that is @'s have exactly one left neighbour so, all of them have any of the 2 colours that is not possessed by their left neighbours, thus all of them will have 2 choices.
Which gives 3x2x2x2x2 = 48.
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