Difference between revisions of "2012 AMC 10B Problems/Problem 11"

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[[2012 AMC 10B Problems/Problem 11|Solution]]
 
[[2012 AMC 10B Problems/Problem 11|Solution]]
 
 
 
== Solutions ==
 
We have 4 choices for desserts.
 
 
However, the same dessert cannot be served for 2 straight days, meaning that you only have 3 choices for a dessert for the next day.
 
It is also given that there must be cake on Friday.
 
 
So,
 
 
<math>4*3*3*3*3*1*3=\boxed{972}</math>
 
 
OR
 
 
 
<math> \textbf{(B)}</math>
 

Revision as of 18:47, 24 February 2012

Problem 11

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?

$\textbf{(A)}\ 729\qquad\textbf{(B)}\ 972\qquad\textbf{(C)}\ 1024\qquad\textbf{(D)}\ 2187\qquad\textbf{(E)}\2304$ (Error compiling LaTeX. Unknown error_msg)

Solution