(i) Find the number of trees on n vertices in which a given vertex is an end-vertex. (ii) Deduce that, if n is large, then the probability that a given vertex of a tree with n vertices is an end-vertex is approximately e-l.

A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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10.3
(i)
Find the number of trees on n vertices in which a given vertex is an end-vertex.
(ii)
Deduce that, if n is large, then the probability that a given vertex of a tree with n
vertices is an end-vertex is approximately e-!.
Transcribed Image Text:10.3 (i) Find the number of trees on n vertices in which a given vertex is an end-vertex. (ii) Deduce that, if n is large, then the probability that a given vertex of a tree with n vertices is an end-vertex is approximately e-!.
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