Difference between revisions of "2006 AMC 10A Problems/Problem 25"

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== Problem ==
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#redirect [[2006 AMC 12A Problems/Problem 20]]
A bug starts at one [[vertex]] of a [[cube (geometry) | cube]] and moves along the [[edge]]s of the cube according to the following rule. At each vertex the bug will choose to travel along one of the three edges emanating from that vertex. Each edge has equal [[probability]] of being chosen, and all choices are independent. What is the probability that after seven moves the bug will have visited every vertex exactly once?
 
 
 
<math>\mathrm{(A) \ } \frac{1}{2187}\qquad\mathrm{(B) \ } \frac{1}{729}\qquad\mathrm{(C) \ } \frac{2}{243}\qquad\mathrm{(D) \ } \frac{1}{81}\qquad\mathrm{(E) \ } \frac{5}{243}\qquad</math>
 
== Solution ==
 
{{solution}}
 
== See Also ==
 
*[[2006 AMC 10A Problems]]
 
 
 
*[[2006 AMC 10A Problems/Problem 24|Previous Problem]]
 
 
 
[[Category:Introductory Geometry Problems]]
 
[[Category:Introductory Combinatorics Problems]]
 

Latest revision as of 15:43, 11 July 2020

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