2012 AMC 12B Problem 8
Problem 8 of 25EasierCounting & Probability
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?
Answer choices
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Solution
Friday is fixed as cake. Work outward from Friday.
Each of the other six days (Saturday, then Thursday, Wednesday, Tuesday, Monday, Sunday) can be any dessert except the one served on the neighboring already-chosen day, giving choices each.
The number of menus is
Thus, the correct answer is A.