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Different colorings of pentagon

Source: 2011 AMC A Problem 22

June 25, 2011
geometrygeometric transformationrotationsymmetryAMC

Problem Statement

Each vertex of convex pentagon ABCDEABCDE is to be assigned a color. There are 66 colors to choose from, and the ends of each diagonal must have different colors. How many different colorings are possible?
<spanclass=′latex−bold′>(A)</span> 2520<spanclass=′latex−bold′>(B)</span> 2880<spanclass=′latex−bold′>(C)</span> 3120<spanclass=′latex−bold′>(D)</span> 3250<spanclass=′latex−bold′>(E)</span> 3750 <span class='latex-bold'>(A)</span>\ 2520\qquad<span class='latex-bold'>(B)</span>\ 2880\qquad<span class='latex-bold'>(C)</span>\ 3120\qquad<span class='latex-bold'>(D)</span>\ 3250\qquad<span class='latex-bold'>(E)</span>\ 3750
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