Exam 5 Solutions Math 375 Spring 2014
Name:
Instructions: Solve the following problems using the techniques discussed
in class.
1. In class I introduced the n-dimensional hypercube Qn . Its vertex set
Exam 1 Math 375 Spring 2014
Name:
Instructions: Write one answer per blank sheet of paper.
1. The Math Club consists of three freshmen, four sophomores, and six juniors. A team of ve people is selecte
Exam 2 Solutions Math 375 Spring 2014
Name:
Instructions: Write one answer per blank sheet of paper.
1. The partition 7 + 5 + 4 + 4 is an example of a partition of 20 in which
the rst part (7) is grea
Exam 4 Solutions Math 375 Spring 2014
Name:
Instructions:
1. The complete graph on 100 vertices, K100 , has 100 = 4950 edges and
2
100
= 75287520 copies of K5 in it. Prove that no matter which 494 edg
Chapter 3 Supplementary Exercise Answers
(25) 243
(26) 210
(27) 2n1
(28) 2n 2n2
(29) 200
(30) 4536
(31) 3168
(32) 450
(33a) n!
4
(33b) n!
3
(34) If n is odd the answer is 0 If n = 2k the answer is 2k
Chapter 4 Additional Problems
62. Evaluate
n
k=1
n
k=1
63. Evaluate
n
n
5k+2
k=1 k (k+1)(k+2) .
61. Evaluate
n k
3 .
k
k 2 n 4k .
k
k
64. Find the binomial identity that can be obtained by counting su
Chapter 4 Supplementary Exercise Answers
(28) (31) skip
(32)
n+k
n
.
(33) (37) skip
(38) Special case of Theorem 4.7 (p. 71) with
number n .
i
n
ni
replaced by the equivalent
(39) Same as (38) but now
Exam 3 Solutions Math 375 Spring 2014
Name:
Instructions: In the questions below, you are asked to prove that a generating function has a particular form. A proof consists of using the generating
func