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2012 AMC 12B Question 8

AMC12 · 2012 AMC 12B

Question 8

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?
  1. $729$
  2. $972$
  3. $1024$
  4. $2187$
  5. $2304$