Math 484
Problem Set #5 Solution
7 March 2014
1. Let S10 denote the set of permutations of 10.
(a) How many 5-cycles are there in S10 ?
Solution: Here is a solution in the spirit of Bender & Williamso
Math 484
Problem Set #1 Solution
5 February 2014
1. Use the Rule of Product (Theorem 1.2) to count the number of even four-digit positive
integers. Explain how the even four-digit positive integers co
Math 484
Problem Set #3 Solution
24 February 2014
1. (a) Use a spreadsheet program to construct a table of the Stirling numbers of the
cfw_
n
second kind,
, for 1 n 10, and 1 k 10.
k
(This was the las
Math 484
Problem Set #6 Solution
14 March 2014
1. We decorate the vertices of a regular pentagon using one white bead, two black beads,
(
)
5
and two red beads. If the pentagon is xed, then there are
Math 484
Problem Set #2 Solution
12 February 2014
1. Consider an ordinary deck of 52 playing cards supplemented by two wild cards, W1 and
W2. In a poker hand, a wild card can be used as any card (incl
Math 484
Problem Set #4 Solution
28 February 2014
1. (B&W Exercise 1.4.8) For each n > 0, let Bn denote the total number of partitions of
n. That is,
cfw_ cfw_
cfw_
n
n
n
Bn =
+
+ +
.
1
2
n
For conven
Math 484
Problem Set #7 Solution
28 March 2014
1. A cube has twelve edges. The symmetry group of the cube has
24 elements. One element is the identity, and there are four other
types of elements (tech