A game designer must decide how to color four buildings that are in a row. Using only the colors yellow, green, red, and blue, each building must be painted with exactly one color. Any two neighboring buildings must be different colors, and the first and last buildings must be different colors. How many ways are there to paint the four buildings? PLS HELP 55PTS!!!

4 buildings and 4 colors.

First building can be 1 of 4 colors

Second building can be 1 of 3 colors because it can't be the same color as the first building.

Third building can be 1 of 3 colors because it can't be the same color as the 2nd building.

The forth building can be 1 of 2 colors because it can't be the same color as the first or third buildings.

Total combinations: 4 x 3 x 3 x 2 = 72 different ways.

a

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