Faculty of Economics and Political Science
Department of Statistics
First Year (Credit Hours System)
Principles of Mathematics (S103)
Fall 2021
Sheet (2)
1- In a production process, a product goes through one of the assembly lines A, B, or C
and then goes through one of the finishing lines D or E. Draw a tree diagram that
indicates the possible production routes for a unit of the product. How many
production routs are possible?
2- Determine the values 6 P3 and 6 P3 4P3 .
3- Determine the value 6C4 , 5 P3 4 C2 ,
100
C100 .
4- A red die is rolled and then a green die is rolled. How many results are possible?
5- A coin is tossed 3 times. Draw a tree diagram to indicate the possible results and
determine how many results are possible?
6- A student must take a mathematics course, a laboratory science course, and a
humanities course. The available mathematics classes are category theory, measure
theory, and real analysis. The laboratory science possibilities are astronomy, biology,
chemistry, geology, and physics. In humanities, the available courses are classics,
English, French, and history. How many three-course selections can the student make?
7- A person lives in city A and commutes by automobile to city B. There are five roads
connecting A and B.
a) How many routes are possible for a round trip?
b) How many round-trip routes are possible if a different road is to be used for the
return trip?
8- A Canadian postal code consists of a string of six characters, of which three are letters
and three are digits, which begins with a letter and for which each letter is followed by
a (single) digit. (For readability, the string is broken into strings of three. For example,
-1-
B3H3J5 is a valid postal code). How many Canadian postal codes are possible? How
many of these begin with B3H?
9- On a history exam, each of six items in one column is to be matched with exactly one
of eight items in another column. No item in the second column can be selected more
than once. In how many ways can the matching be done?
10-
A combination lock has 26 different letters, and a sequence of three different
letters must be selected for the lock to open. How many combinations are possible?
11- How many six letter words form the letters in the word MEADOW are possible if no
letter repeated?
12- In how many ways can a five-member committee be formed from a group of 19
people?
13- In a 10 question examination. Each question is worth 10 points and is graded right or
wrong. Considering the individual questions in how many ways can a student score
80 or better?
14- A sports team plays 11 games. In how many ways can the outcomes of the games
result in 4 wins, 5 losses, and 2 ties?
15- A little league baseball team has 12 members and must play an away game. Three
cars will be used for transportation. In how many ways can the manager assign the
members to specific cars if each car can accommodate 4 members?
16- A social services office has 15 new clients. The supervisor wants to assign 5 clients
to each of three specific caseworkers. In how many ways can this be done?
17- There are 11 members on a hockey team, and all but one, the goalie, are qualified for
the other five positions. In how many ways can the coach form a starting lineup?
18- A committee has seven members 3 are males and 4 are females. In how many ways
can a subcommittee be selected if it is to consist exactly of
a- Three males
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b- Four females
c- Two males and two females
19- A committee has 3 male and 5 female members. In how many ways can a
subcommittee of four be selected if at least 2 females are to serve on it?
20- A waiter takes the following order from a table with seven people: three hamburgers,
two cheeseburgers, and two steak sandwiches. Upon returning with the food, he
forgets who ordered what item and simply places an item in front of each person. In
how many ways can the waiter do this?
21- A paint manufacturer wishes to manufacture several different paints. The categories
include
Color: red, blue, white, black, green, brown, yellow
Type: latex, oil
Texture: flat, semigloss, high gloss
Use: outdoor, indoor
How many different kinds of paint can be made if you can select one color, one
type, one texture, and one use?
22- The advertising director for a television show has 7 ads to use on the program. If she
selects 1 of them for the opening of the show, 1 for the middle of the show, and 1 for
the ending of the show, by how many possible ways can this be accomplished?
23- A newspaper editor has received 8 books to review. He decides that he can use 3
reviews in his newspaper. How many different ways can these 3 reviews be selected?
24- A school musical director can select 2 musical plays to present next year. One will be
presented in the fall, and one will be presented in the spring. If she has 9 to pick
from, how many different possibilities are there?
25- In a club there are 7 women and 5 men. A committee of 3 women and 2 men is to be
chosen. How many different possibilities are there?
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26- A store has 6 TV Graphic magazines and 8 Newstime magazines on the counter. If
two customers purchased a magazine, find the probability that one of each magazine
was purchased.
27- By how many ways can you arrange 6 books in the following cases:
a.
if the arrangement is in a row on a shelf
b.
if the arrangement is on a round shelf
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