14. An ice cream shop has a special on banana splits, and Xing is taking advantage of it. Hes
astounded at all the options he has in constructing his banana split:
He must choose three different flav
FINAL EXAM SOLUTIONS
Student Name and ID Number
MATH 3012 Final Exam, December 15, 2010, WTT
Note. The answers given here are more complete and detailed than students are expected to
provide when taki
MATH 3012 A
Summer 2012
Homework 6
Due 07/18/2012
1. Can a simple graph have 5 vertices, each with degree 6?
(5)
2. A graph has 21 edges, has 7 vertices of degree 1, three of degree 2, seven of degree
MATH 3012 Homework Problems and Solutions Chapter 2, Spring 2009, WTT and MTK
Note: These problems are grouped into two categories. The rst set consists of basic problems that everyone who expects to
Applied Combinatorics
Preliminary Edition
February 15, 2015
Mitchel T. Keller
Washington & Lee University
William T. Trotter
Georgia Institute of Technology
Copyright c 20082015 Mitchel T. Keller and
Applied Combinatorics
Preliminary Edition
January 5, 2014
Mitchel T. Keller
Washington & Lee University
William T. Trotter
Georgia Institute of Technology
Copyright c 2014 Mitchel T. Keller and Willia
Math 3012-N2 Practice Final
The final will be administered in Weber SST Lecture Hall 2, 8am-10:50am Monday December
9 2013. You will be allowed to bring to the final a single (double-sided) 8.5 11 inc
319 /ugm
Student Name and ID Number
MATH 3012 Quiz 1, September 18, 2014, WTT
1.
@a.
W
b.
C.
(:1.
Consider the 26 element set consisting of the capital letters of the English alphabet: cfw_A, B, 0,. Z
MATH 3012 C
Midterm 3 Review
April 18, 2016
1. How many positive integers not exceeding 100 are either odd or the square of an integer?
Solution: The space is cfw_1, 2, . . . , 100. Consider the prope
MATH 3012 C
Midterm 2
March 11, 2016
Name:
Directions: Show all work. Partial credit depends on it. Where justification is required, correct answers
without proper evidence of understanding will not r
MATH 3012 C
Midterm 1
February 12, 2016
Name:
Row #:
Directions: You have 50 minutes to complete this individual exam. There are 100 possible points. Correct answers
without proper evidence of underst
MATH 3012 C
Solutions to Review for Midterm 2
March 2, 2016
1. In how many ways can a 2 n rectangular checkerboard be tiled using 1 2 and 2 2 pieces? Find a
closed formula.
Solution:
If tn is the numb
MATH 3012 C
Review for Midterm 1
February 5, 2016
1. There is an M&M store in Times Square that sells the 6 standard colors of M&Ms. The M&Ms are
separated into large bins so that people can chose the
MATH 3012 C
Review for Midterm 2
March 2, 2016
1. In how many ways can a 2 n rectangular checkerboard be tiled using 1 2 and 2 2 pieces? Find a
closed formula.
2. Let s(n + 1) = 2s(n) + 3n2 with s(1)
Student Name and ID Number
MATH 3012 Final Exam, December 11, 2014, WTT
1. Consider the 11-element set X consisting of the three capital letters cfw_A, B, C and the eight
digits cfw_0, 1, 2, . . . , 7
PRACTICE PROBLEMS FOR MIDTERM 3
MATH 3012-C, FALL 2015
sh is
ar stu
ed d
vi y re
aC s
o
ou urc
rs e
eH w
er as
o.
co
m
The real exam will contain 1-2 proofs, short answer questions, 3 computational qu
Midterm 1, Math 3225, Fall 2010
October 13, 2010
1. Define the following terms.
a. The three Kolmogorov axioms of probability (list them).
b. sigma algebra.
c. Binomial distribution (write out the pdf
1W
14
1514
52/107927
Student Name and ID Number
MATH 3012, Quiz 3, November 25, 2014, WTT
1. a. In terms of partitions of an integer, interpret the meaning of the coefcient of x47 in the
following gen
SEO/M'lb
Student Name and ID Number
MATH 3012, Quiz 3, November 24, 2015, WTT
1. Let n and m be positive integers with n 2 m.
\ a. Write the inclusion/ exclusion formula for the number S(n, m) of surj
Math 3012-N2 Practice Final
The final will be administered in Weber SST Lecture Hall 2, 8am-10:50am Monday December
9 2013. You will be allowed to bring to the final a single (double-sided) 8.5 11 inc
Math 3012-N Name: Lj On
Fall 2015, Dr. Greenwood
Midterm 2 Make-Up
October 22, 2015
This exam contains 7 questions worth 10 points each, for a total of 70 points.
The exam is closedbook. You may not
Math 3012-N Name: 3%
Fall 2015, Dr. Greenwood
Midterm 3
November 13, 2015
#
This exam contains 7 questions for a total of 100 points.
The exam is closedbook. You may not use any outside sources.
Score
Math 3012-N Name
Fall 2015, Dr. Greenwood
Midterm 3 Make-up
November 19, 2015
This exam contains 7 questions for a total of 100 points.
The exam is closedbook. You may not use any outside sources.
Course Topics
Math 3012-N
The following is a (potentially non-exhaustive) list of important topics we have studied over the semester,
meant to give you an idea of what you should know for the final ex
PRACTICE PROBLEMS FOR MIDTERM 3
MATH 3012-C, FALL 2015
The final exam covers material from throughout the semester. These practice exams are not
guareenteed to be comprehensive.
1. Definitions
a) A fu
PRACTICE PROBLEMS FOR MIDTERM 2
MATH 3012-C, FALL 2015
The real exam will contain 4 definitions, 1 proof, short answer questions, 2 computational questions, an algorithm question, and true/false.
1. C
Sp/uhon 5
Student Name and ID Number
MATH 3012 Quiz 2, October 28, 2014
1. In the space to the right, use the algorithm developed in class (always proceed to the lowest
legal vertex) to nd an Euler ci
SO/Z/LfIZH/J
Student Name and ID Number
MATH 3012, Quiz 3, April 19, 2013, WTT
1. A single die (six sides) is rolled. If the result is a one, two or three, the payoff is $4. If the result
is a four or
30 /M 790/421
Student Name and ID Number
MATH 3012 Final Exam, December 8, 2015, WTT
1. Consider the 36- element set X consisting of the twenty-six capital letters of the English alphabet
and the te
MATH 3012 Fall 2016, Final Exam Sample: Closed book, no calculators.
Instructor: Esther Ezra.
This sample contains twelve questions, your exam will contain only ten.
Answer all questions on these shee
30 /M 790/421
Student Name and ID Number
MATH 3012 Final Exam, December 8, 2015, WTT
1. Consider the 36- element set X consisting of the twenty-six capital letters of the English alphabet
and the te
MATH 3012 Fall 2016, Midterm Exam 1, Oct 5 2016
Instructor: Esther Ezra.
Closed book, no calculators
Name
GT IDnumber
Problem 1. (25 points) Consider the alphabet consisting of the ten digits cfw_0, 1
Figure 1:
MATH 3012 Fall 2016, Midterm Exam 2, Nov 16 2016
Instructor: Esther Ezra.
Closed book, no calculators
Name
GT IDnumber
Problem 1. (25 points) Consider the graph G in Figure 1.
a. (5 points)