MAT 344
Challenge Set 1
The following questions illustrate some counting principles that will be discussed in this
course. Try to prove your answer carefully. Where all else fails, enumerate the possibilities
and see if you can discover the general counti
Welcome to MAT 344: Introduction to Combinatorics
Draft Course Outline To be finalized
Instructor: Prof. Steve Tanny
email: tanny@math.utoronto.ca
Office: Bahen Centre 6187
Tel: 416-978-3324
Contact: Email, skype, usual office hours W: 10-11, 3-4:30; R:10
MAT344
Professor S. Tanny
Enumerative Combinatorics . . . How do I love thee? Let me count
the ways! (E. B. Browning)
Count the number of elements in a (nite) set, or the number of ways of
arranging the elements of nite sets into denite patterns. For exam
MAT 344
Challenge Set 2
The following is a selection of problems that you will nd useful to test your understanding
of the enumeration concepts we have been studying. There are more in the text that are also
worthwhile, and you are encouraged to select ad
MAT 344
Quiz 1 Solutions
September 25, 2009
You can see that all of these problems can be solved by extension. But,
what if you had a library of 85 languages, or a casino with thousands of
dice being rolled every hour? You will have to come up with a smar
MAT 344
Quiz 2 Solutions
October 19, 2007
Question 1: Prove using a combinatorial argument that
n
2n
2
=
2
2 +n .
2
(10 points)
Some people did not give a combinatorial proof of the identity. You must
learn the combinatorial arguments. Others gave an exam
MAT 344
Quiz 4 Solutions
November 7, 2009
Question 1: How many ways are there to make an r-arrangement of
pennies, nickels, dimes, and quarters using any number of nickels and
dimes, at least one penny, and an odd number of quarters? (Coins of the
same de
MAT 344
Quiz 4
November 20, 2009
Question 1: Use the method of generating functions to solve completely
the recursion: for n 1 hn = 2hn1 + 1, and h0 = 1 (10 points).
Note: No credit will be given for a solution that does not use this method.
Answer 1:
hn
University of Toronto
MAT344 Midterm Examination
Question 1: Suppose that a computer selects two songs at random, one from each
the album: A Top 10, LtnJzz and B Ltn 41 s most asked. The list of each album is:
A
Song
Musician
B
Song
Musician
1
2
3
4
5
6
7