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The ordered list 1,2,3,4,5,6,7,8 each number is painted with one of the colors blue (B), Purple...

The ordered list 1,2,3,4,5,6,7,8 each number is painted with one of the colors blue (B), Purple (P), Yellow (Y) and Grey (G). How many different ways can they be colored if two consecutive numbers can't have the same color? (Its possible for one of the colors to not be used). Explain the calculations.

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Answer #1

number of ways to color =N(4 choice for first, 3 for 2nd(except the color with which first is painted  , 3 for 3rd (except with which 2nd one is painted ) and so on)

=4*3*3*3*3*3*3*3 =8748

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