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# help

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Four houses in a row are each to be painted with one of the colors red, blue, green, and yellow. In how many different ways can the houses be painted so that no two adjacent houses are of the same color?

Jan 25, 2020

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Four houses in a row are each to be painted with one of the colors red, blue, green, and yellow.

In how many different ways can the houses be painted so that no two adjacent houses are of the same color?

$$\begin{array}{|c|c|c|} \hline \text{House} & \text{selectable colors}& \text{number of selectable colors} \\ \hline A & red,~ blue,~ green,~ yellow & 4 \\ \hline B & not~A & 3 \\ \hline C & not~B & 3 \\ \hline D & not~C & 3 \\ \hline && \text{product}~ 4\times 3 \times 3 \times 3 = 108 \\ \hline \end{array}$$

The houses can be painted in 108 different ways.

Jan 25, 2020