Discrete Structure Graph and Tree a) How many edges does a full 5-ary tree with 121 leaves have?b) How many vertices does a full 7-ary tree with 121 internal vertices have?c) Tis a binary tree of height 3. What is the largest and smallest number of nodes that T canhave?d) The futsal tournament follows a single-elimination format in which a team is eliminated afterone loss. Suppose the results of the tournament are represented in a binary tree. If thetournament is limit only 5 rounds of games to determine the winner, how many teams can beregistered for the tournament and how many matches need to schedule by the organizer?

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Answered: a) How many edges does a full 5-ary…

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter2: Parallel Lines

Section2.5: Convex Polygons

Problem 41E

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Consider a full 4-ary tree.• If there are 5 internal vertices, find the total number of vertices and the number of leaves • If there are 5 vertices, find the number of internal vertices and the number of leaves• If there are 7 leaves, find the total number of vertices and the number of internal vertices
An experiment consists of tossing a die and then flipping a coin once if the number on the die is even. If the number on the die is odd, the coin is flipped twice. Using the notation 4H, for example, to denote the outcome that the die comes up 4 and then the coin comes up heads, and 3HT to denote the outcome that the die comes up 3 followed by a head and then a tail on the coin, construct a tree diagram to show the 18 elements of the sample space S.
At a corporation, an employee can build a computer system using one of four monitors, one of two keyboards, andone of three computers. Draw a tree diagram to illustrate the dierent possible choices (use M1, M2, M3, M4 forthe monitors, and so on) and calculate the number of computer systems one can build.
Consider the following tree for a prefix code Figure 13: A tree with 5 vertices. The top vertex branches into character, a, on the left, and a vertex on the right. The vertex in the second level branches into character, e, on the left, and a vertex on the right. The vertex in the third level branches into two vertices. The left vertex in the fourth level branches into character, c, on the left, and character, n, on the right. The right vertex in the fourth level branches into character, d, on the left, and character, y, on the right. The weight of each edge branching left from a vertex is 0. The weight of each edge branching right from a vertex is 1. Use the tree to decode “11100110111001000
Consider a full 4-ary tree.• If there are 7 leaves, find the total number of vertices and the number of internal vertices
Consider a full 4-ary tree.• If there are 5 internal vertices, find the total number of vertices and the number of leaves
How many perfect matchings does the “ladder” with 2n nodes (Figure 10.11) have?
. Consider a full 4-ary tree.• If there are 5 vertices, find the number of internal vertices and the number of leaves
How many vertices does a full 5-ary tree with 100 internal vertices have?
Assume the cards are drawn sequentially and without replacement. (permutations)In how many ways can 5 spades be drawn from a standard deck of 52 cards?
Draw a complete ternary tree of height 3. How many nodes does the tree have?
A person with $2 in her pocket bets $1, even money,on the flip of a coin, and she continues to bet $1 as longas she has any money. Draw a tree diagram to show thevarious things that can happen during the first four flipsof the coin. After the fourth flip of the coin, in how manyof the cases will she be(a) exactly even;(b) exactly $2 ahead?

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