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Let T = (V , E) be a tree with |V | = n ≥ 2. How many distinct paths are there (as sub graphs) in T?

I already have the answer to this question as (n/2). The problem that I'm having is finding anything in the text that helps me to figure out how to arrive at this answer.

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closed as no longer relevant by Gerry Myerson, Chris Godsil, Mark Sapir, Benoît Kloeckner, Brendan McKay Jun 24 '13 at 13:45

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1 Answer

Any two vertices of a tree are connected by a unique path, so there are exactly $n\choose2$ paths of length at least one.

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Good job. That wasn't too hard. :-) If you want, you can accept your own answer as the "correct answer". For that, click on the check mark next to your answer. –  André Henriques Jun 22 '13 at 21:53
    
@ButchMalahide: wait what? I think the answer is right, there are n choose 2 paths of length at least one. –  Zsbán Ambrus Jun 23 '13 at 9:49
    
I think maybe the disagreement is semantic, whether we take the length to be the number of vertices or the number of edges. –  Eric Tressler Jun 23 '13 at 9:51
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