Question 3: Consider a single elimination tournament of 16 football teams, laid out as in the diagram below. Once a team loses it is out of the tournament. Every team must play until it is eliminated. The starting positions for each team are fixed. A matchup (X,Y) represents a game between teams X and Y. A round is the set of all the matchups at a given stage of the tournament (the matchups above the round title in the diagram). Thus round 3 in the diagram below is the set {(D, E), (I,O)} of matchups. An outcome is the union of all the matchups along with the winner. (Essentially two outcomes are different if the winners of the games produce a different letter in at least one place in the diagram below.) A A B C D E F G H D E G D E Round 1 Round 2 Round 3 D WINNER Round 4. O L N Round 3 Round 2 Round 1 -J -K

Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
icon
Related questions
Question
Question 3: Consider a single elimination tournament of 16 football teams, laid out as in
the diagram below. Once a team loses it is out of the tournament. Every team must play
until it is eliminated. The starting positions for each team are fixed. A matchup (X,Y)
represents a game between teams X and Y. A round is the set of all the matchups at a
given stage of the tournament (the matchups above the round title in the diagram). Thus
round 3 in the diagram below is the set {(D, E), (I,O)} of matchups. An outcome is the
union of all the matchups along with the winner.
(Essentially two outcomes are different if the winners of the games produce a different
letter in at least one place in the diagram below.)
A
A
B
C
D
E
F
G
H
D
E
G
D
E
Round 1 Round 2 Round 3
D
WINNER
Round 4
O
L
N
-J
-K
Round 3 Round 2 Round 11
a) How many unique outcomes are there in this tournament?
b) How many unique outcomes are there where A wins the entire tournament?
c) How many unique outcomes are there where D never faces E?
-M
Transcribed Image Text:Question 3: Consider a single elimination tournament of 16 football teams, laid out as in the diagram below. Once a team loses it is out of the tournament. Every team must play until it is eliminated. The starting positions for each team are fixed. A matchup (X,Y) represents a game between teams X and Y. A round is the set of all the matchups at a given stage of the tournament (the matchups above the round title in the diagram). Thus round 3 in the diagram below is the set {(D, E), (I,O)} of matchups. An outcome is the union of all the matchups along with the winner. (Essentially two outcomes are different if the winners of the games produce a different letter in at least one place in the diagram below.) A A B C D E F G H D E G D E Round 1 Round 2 Round 3 D WINNER Round 4 O L N -J -K Round 3 Round 2 Round 11 a) How many unique outcomes are there in this tournament? b) How many unique outcomes are there where A wins the entire tournament? c) How many unique outcomes are there where D never faces E? -M
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps

Blurred answer
Knowledge Booster
Polynomial time
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, computer-science and related others by exploring similar questions and additional content below.
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
Database System Concepts
Database System Concepts
Computer Science
ISBN:
9780078022159
Author:
Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:
McGraw-Hill Education
Starting Out with Python (4th Edition)
Starting Out with Python (4th Edition)
Computer Science
ISBN:
9780134444321
Author:
Tony Gaddis
Publisher:
PEARSON
Digital Fundamentals (11th Edition)
Digital Fundamentals (11th Edition)
Computer Science
ISBN:
9780132737968
Author:
Thomas L. Floyd
Publisher:
PEARSON
C How to Program (8th Edition)
C How to Program (8th Edition)
Computer Science
ISBN:
9780133976892
Author:
Paul J. Deitel, Harvey Deitel
Publisher:
PEARSON
Database Systems: Design, Implementation, & Manag…
Database Systems: Design, Implementation, & Manag…
Computer Science
ISBN:
9781337627900
Author:
Carlos Coronel, Steven Morris
Publisher:
Cengage Learning
Programmable Logic Controllers
Programmable Logic Controllers
Computer Science
ISBN:
9780073373843
Author:
Frank D. Petruzella
Publisher:
McGraw-Hill Education