18.440 PROBLEM SET ONE, DUE SEPTEMBER 18
A. FROM TEXTBOOK CHAPTER ONE:
1. Problems: 10, 17, 20, 32, 33.
2. Theoretical Exercises: 12, 13, 18, 20.
3. Self-Test Problems and Exercises: 14.
B. Compute the following as functions of n:
1.
n
X
k
2
k=0
2.
2n
X
k
(−1)
k=n+1
n
k
2n
k
.
.
C. Answer the following:
1. How many orderings the cards in a standard deck of 52 cards (26
black, 26 red) strictly alternate between red and black (i.e., no two
reds or two blacks in a row)?
2. (*) How many orderings have the property that there are no two
cards of the same suit (there are 13 cards in each of 4 suits) in a row?
1