Chapter 5 Supplementary Exercise Answers, p. 106:
(17) 8192
(18) 94828
(19) 92
(21) Divide each even part by 2.
(23) 16
(24) 1001
(27)
(n2)(n1)n(3n5)
24
(28) n
6 11n5 +47n4 97n3 +96n2 36n
48
(32) F (n + 1) =
n1 n
i=0 i
=
(n3)2 (n2)2 (n1)n
48
F (i) where F
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
consists of all 2n binary strings of length n (sequenc
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 selected from the club for a math competition.
The team must i
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 greater than the number of parts (4). The partition
4 + 4 +
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 edges
5
you delete from K100 , the resulting graph has at
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 subsets of
[n] that contain a red number, a blue number,
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 introducing a circled dot where needed.
(40) Binomial
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
function models we have discussed in class to derive the pr