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An ant is walking on a hexagon. At each step, he moves from the vertex on which he is standing to an adjacent vertex. After \(8\) steps, what is the probability that he is standing on the same vertex on which he began?

 Feb 15, 2022
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First to calculate probability, we have total number of restricted ways/total number of possibilities. Since he moves 8 steps, and there are only 2 possible locations adjacent to which he can go, there are 8^2 = 64 TOTAL possibilities. 

 

There are 8 steps, and 5 other vertices in the hexagon to go from.

 

Maybe this information could get you started... :) 

 Feb 15, 2022

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