Dr. A. Betten
Fall 2009
MATH 501 Introduction to Combinatorial Theory
Assignment # 1
Problem # 1
How many positive integers less than 10n (in decimals) have their digits in
nondecreasing order?
Problem # 2
What is the maximum length of a binary string (of 0’s and 1’s) such that
no two substrings of length three are the same? Give an example of such a
string.
Problem # 3
Consider your first name with letters replaced by numbers (’a’=0, ’b’=1,
etc.). After deleting repetions and diregarding the ordering of the letters
your have a subset of Z26 = {0, 1, . . . , 25}. Compute the rank of this subset
in the lexicographical ordering.
Problem # 4
Find the subset ranked 800 (when counting from 0) in the power set of Z10 .