Answer to Question #207783 in Discrete Mathematics for Natasha

Question

Calculate the number of vertices in a full 5-ary tree with 45 internal vertices.Also find out the number of leaves.

Answer 1

A full $m$ ‐ary tree with $i$ internal vertices has $n=m\cdot i+1$ vertices. 

$$n=m\cdot i+1=5\cdot 45+1=226$$

A full $m$ ‐ary tree with $i$ internal vertices has $l=(m-1)i+1$ leaves.

$$l=(m-1)i+1=(5-1)\cdot45+1=181$$