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

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== Problem ==
#redirect [[2006 AMC 12A Problems/Problem 20]]
A bug starts at one vertex of a cube and moves along the edges 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 ==
== See Also ==
*[[2006 AMC 10A Problems]]
*[[2006 AMC 10A Problems/Problem 24|Previous Problem]]
[[Category:Introductory Geometry Problems]]

Latest revision as of 14:43, 11 July 2020

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