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Dessert Chef and Yummy Desserts

Source: 2012 AMC10B Problem #11

February 23, 2012
symmetryrotationAMC

Problem Statement

A dessert chef prepares the dessert for every day of a week starting with Sunday. The dessert each day is either cake, pie, ice cream, or pudding. The same dessert may not be served two days in a row. There must be cake on Friday because of a birthday. How many different dessert menus for the week are possible?
<spanclass=latexbold>(A)</span> 729<spanclass=latexbold>(B)</span> 972<spanclass=latexbold>(C)</span> 1024<spanclass=latexbold>(D)</span> 2187<spanclass=latexbold>(E)</span> 2304 <span class='latex-bold'>(A)</span>\ 729\qquad<span class='latex-bold'>(B)</span>\ 972\qquad<span class='latex-bold'>(C)</span>\ 1024\qquad<span class='latex-bold'>(D)</span>\ 2187\qquad<span class='latex-bold'>(E)</span>\ 2304