1.) A product can be shipped by
four airlines and each airline can ship via three different routes. How many distinct ways exist to ship the
product?
2.) How many different license
plates can be made if each license plate is to consist of three letters
followed by three digits with replacement?
Without replacement?
3.) How many different license
plates can be made if each license plate begins with 63 followed by three
letters and two digits?
4.) Marie is planning her
schedule for next semester. She must
take the following five courses:
English, history, geology, psychology, and mathematics.
a.) In how many different ways
can Marie arrange her schedule of courses?
b.) How many of these schedules
have mathematics listed first?
5.) You are given the set of
digits {1, 3, 4, 5, 6}.
a.) How many three-digit numbers
can be formed?
b.) How many three-digits
numbers can be formed if the number must be even?
c.) How many three-digits
numbers can be formed if the number must be even and no repetition of digits is
allowed?
1.) A certain Math 110 teacher
has individual photos of each of her three dogs: Indy, Sam, and Jake. In how many ways can she arrange these photos
in a row on her desk?
2.) If seven people board an
airplane and there are nine aisle seats, in how many ways can the people be
seated if they all choose aisle seats?
3.) A disc jockey can play eight
records in a 30-minute segment of her show.
For a particular 30-minute segment, she has 12 records to select
from. In how many ways can she arrange
her program for the particular segment?
4.) Two co-chairpersons are to
be selected from a group of nine eligible people. In how many ways can this be done?
5.) How many distinct
arrangements can be formed from all the letters of SHELTONSTATE?
6.) In how many distinct ways
can the letters of MATHEMATICS be arranged?
Mixed
Practice
7.) A club of 20 people is going
to elect a chairperson and a secretary.
In how many different ways can this be done?
8.) Mike has 8 pullovers and 6
pairs of pants. How many outfits does he
have to choose from?
9.) A primary zip code is a
five-digit numeral. How many of these
zip codes can be formed is no digit can be repeated? How many of these zip codes can be formed if
repetition is allowed?
10.) In Riverhead there are 5
roads leading to a traffic circle. In
how many ways can a driver enter the traffic circle by one road and leave by
another?
11.) Given the set of digits {4,
5, 6, 7, 8, 9}, how many three-digit numbers can be formed if no digit can be
repeated? How many three-digit numbers
can be formed if repetition is allowed?
12.) If there are 50 contestants
in a beauty pageant, in how many ways can the judges award first and second
prizes?
13.) The Southampton Sports Car
Club has 30 members. A slate of officers
consists of a president, a vice president, a secretary, and a treasurer. If a person can only hold one office, in how
many ways can a set of officers be formed?
14.) A baseball manager has eight
pitchers and three catchers on his squad.
In how many ways can the manager select a starting battery (pitcher and
catcher) for a game?
15.) In a room of twenty people,
everyone shakes hands with each other.
How many handshakes are there?
16.) How many four-letter words
can be formed from the set of letters {m, o, n, e, y}? Assume that any arrangement of letters is a
word. How many four-letter words can be
formed if the first letter must be y and the last letter must be m? (Assume no repetition.)
17.) In how many ways can a
basketball coach select a guard and then a center from a squad of 12 players?
18.) Given the set of digits {5,
6, 7, 8, 9}, how many four-digit numbers can be formed if no digit can be
repeated? How many of these will be
odd? How many of these will be divisible
by 5? How many of these will be over
6,000? How many will be over 5,000?
19.) A conference room has four doors. In how many ways can a person enter and leave
the conference room by a different door?
20.) The Rochester Tennis Club is
having a mixed-doubles tournament. If
eight women and their husbands sign up for the tournament, how many
mixed-doubles teams are possible? How
many can be formed if no woman is paired with her husband?
21.) At Finger Lakes Race Track,
there eight horses in each race. The daily
double consists of picking the winning horses in the first and second
races. If a better wanted to purchase
all possible daily double tickets, how many would he have to purchase?
22.) How many different ways can
seven students be seated in seven seats on a subway
car?
23.) A dictionary, an almanac, a
catalog, and a diary are to be placed on a shelf. In how may ways can they be arranged?
24.) In how many distinct ways
can the letters of each word be arranged?
a.)
b.)
c.)
d.)
25.) A traveling book salesperson
has five copies of a certain statistics book, four copies of a certain geometry
book, and three copies of a certain calculus book. If these books are to be stored on a shelf in
the salesperson’s van, how many distinct arrangements are possible?
26.) Almost all students have a
Social Security number. In how many
schools, a student’s Social Security number is also his or her ID number. How many possible Social Security number are
there? (Assume repetition of
digits. A Social Security number contains
nine digits.)
27.) Telephone numbers consist of
seven digits: three digits for the
exchange, followed by four more digits.
In order to call long distance, you must also use an area code, which consists
of three more digits. How many
long-distance telephone number are there if the first
digit cannot be 0 or 1, and the fourth digit cannot be 0 or 1? (Assume repetition of digits.)