Combinatorics (MAD 4203) Fall 2010
Due Wednesday 9/8/2010
Homework #1
1
Prove that if n + 1 numbers are chosen from the set cfw_1, 2, 3, 4, . . . , 2n
then there must be two which dier by 1.
2
Prove that of any ve points chosen within an equilateral trian

MAD 4203, Fall 2010 Some review problems for Midterm #1
These are the problems from Midterm #1 in Fall 2009.
1
A student wants to work exactly 20 days in December, but wants to have at least one of December
25 and December 31 o. In how many ways can the s

Combinatorics (MAD 4203) Fall 2010
Due Wednesday 12/8
Take-home Final Project
If you choose to complete this take-home nal project, it will be counted either as 100
midterm points (like a third midterm), or as 100 homework points, or not counted
at all, w

Combinatorics (MAD 4203) Fall 2010
Due Monday 11/15
Homework #6
Linearity of expectation is a very simple fact with a fancy name; it says that
if X and Y are both random variables (i.e., their values depend on some random
process), then the expected (aver

Combinatorics (MAD 4203) Fall 2010
Due Wednesday 10/27
Homework #5
1
Suppose that n is a multiple of 3. Prove that
c(n, n/3)
n/3
3
n!
.
(n/3)!
(Here c(n, k) is a signless Stirling number of the rst kind, i.e., it
counts the number of permutations of n wi

Combinatorics (MAD 4203) Fall 2010
Due Wednesday 10/20
Homework #4
1
Without using any asymptotic bounds for p(n), prove that p(n) grows
faster than any polynomial. That is, if f (n) is any polynomial, prove
that there is some integer N such that p(n) > f

Combinatorics (MAD 4203) Fall 2010
Due Friday 10/8/2010
Homework #3
1
Find the number of compositions of 25 into ve odd parts.
2
Let an denote the number of compositions of n into parts which are
all greater than 1. Express an in terms of an1 and an2 .
3

Combinatorics (MAD 4203) Fall 2010 Due Wednesday 9/22/2010
Homework #2
1
A school has 105 students, and seven classes. If each student takes
three classes, and each class is taken by the same number of students,
how many students are taking each class?
2

NAME :
MAD 4203 Fall 2010
November 16, 2010
Midterm 2
Instructions: This is a closed book exam and no notes are allowed. You are not to provide or
receive help from any outside source during the exam except that you may ask the instructor for
clarication

NAME :
MAD 4203 Fall 2010
September 24, 2010
Midterm 1
Instructions: This is a closed book exam and no notes are allowed. You are not to provide or
receive help from any outside source during the exam except that you may ask the instructor for
clarication