Homework Set 4
Due Thursday February 10
1. Suppose there are 7 candidates in an election for President of the United
States. Each of 20 people votes for one person.
a. How many election outcomes are possible if an outcome includes not
just the totals, but
EXAM 1 ANSWERS
1. In your own words, explain the pigeonhole principle.
2. There are roughly 300,000 people that pack into New Yorks Time Square on
New Years Eve. Fill in the blanks below (with explanation):
a. At least _ of these people will have the same
Homework Set 1 SOLUTIONS
1. How many people must be chosen to be sure that at least five have the same
last four digits of their cell phone number?
There are 10000 possible 4-digit extensions. The worse case scenario is if
there are 4 people with each of
Homework Set 1
(Due Thursday 1/13)
1. How many people must be chosen to be sure that at least five have the same
last four digits of their cell phone number?
2. (E.C.) Show that at a party of 14 people, there are 2 people who have same
number of friends.
Homework Set 1
(Due Monday 1/14)
1. An employees time clock shows that he worked 81 hours over a period of
10 days. (Note that work time is assigned only in complete hours, not
portions of hours.) Show that on some pair of consecutive days, the
employee w
MTH 398 Homework Set 5 SOLUTIONS
1. In the daily Play 5, players select a number between 00000 and 99999. The lottery
machine contains 5 bins, each with 10 ping-pong balls. Each bin has its ping-pong balls
labeled 0, 1, 2, , 9. The state then randomly sel
Final Exam Review Answers
I did not prove most of these things. I would like you to try to do this on your own.
1. Pigeonhole Principle: Know how to solve basic problems and be able to state what the
principle says (precisely).
There are six math focus c
Final Exam Review Answers
I did not prove most of these things. I would like you to try to do this on your own.
1. Pigeonhole Principle: Know how to solve basic problems and be able to state what the
principle says (precisely).
There are six math focus c
Homework Set 2
Due Thursday 1/20
1. How many integers between 1 and 12,000 inclusive are divisible by none
of 6, 9, and 15?
2. Find the sum of the integers between 1 and 12,000 inclusive that are
divisible by none of 6, 9, and 15?
3. Find the number of in
MTH 398 Homework Set 5 Due Tuesday 2/23
(You will have a quiz on Thursday 2/18)
1. In Connecticut Classic Lotto, you select 6 (different) numbers between 1 and 44. The
Lottery Gods then select 6 different numbers between 1 and 44. You win the Jackpot if
y
EXAM 1 SOLUTIONS
1. Let S be the set of positive integers that are less than or equal to 5680
and are multiples of 8, but are not divisible by 12 or 15.
a. Find the size of S, i.e. |S|.
b. Find the sum of the members in S.
a.
5680
5680 5680 5680
8 LCM
Homework Set 4
Due Thursday February 11
1. Suppose there are 7 candidates in an election for President of the United
States. Each of 20 people votes for one person.
a. How many election outcomes are possible if an outcome includes not
just the totals, but
Homework Set 4
Due Thursday February 10
1. Suppose there are 7 candidates in an election for President of the United
States. Each of 20 people votes for one person.
a. How many election outcomes are possible if an outcome includes not
just the totals, but
Homework Set 3 SOLUTIONS
1. Simple Problems: Please express your answer in the form of (i) P(n,k)
or
n
(ii) or (iii) some other product for some n and k.
k
a. How many ways are there to pick a subset of 7 different letters
from the Greek alphabet?
24
7
Homework Set 3
Due Tuesday January 25
1. Simple Problems: Please express your answer in the form of (i) P(n,k) or
n
(ii) or (iii) some other product for some n and k.
k
a. How many ways are there to pick a subset of 7 different letters from
the Greek alp