MA 114  Introduction to Finite Mathematics
Spring 2021
Instructor
: Lucas Castle
Exam 3  Form A Solutions
1. A publishing company sent out a survey designed to collect information on its consumer base. Of
the 200 respondents, 110 indicated that they were female, 95 were currently attending college, and
125 indicated that they prefer fiction to nonfiction. Looking more closely at the data, it can be
seen that 72 of the respondents were female college students, 63 of the female respondents prefer
fiction to nonfiction, 58 of the college students prefer fiction to nonfiction, and 42 of the female
respondents were college students with a preference for fiction.
(a)
[10 points]
Draw a Venn diagram to represent the publishing company’s survey respondents,
and fill in all regions with appropriate numerical values (i.e. counts).
We already know that 42 of them are female, so that leaves 16 for the remainder of the inter
section [since 58

42 = 16], i.e.
S
16
42
B
A
C
We repeat this process for the females that prefer fiction (we know
n
(
A
∩
C
) = 63) and for the
female college students (we know
n
(
A
∩
B
) = 72). We conclude that
S
16
30
21
42
B
A
C
Finally, we use what we know about the number of elements in
A, B, C,
and
S
to fill in the
remaining regions:
S
21
7
46
16
17
30
21
42
B
A
C
(b)
[10 points]
How many nonfemale respondents prefer fiction over nonfiction?
n
(
A
0
∩
C
) = 16 + 46 = 62
.
2. A local bank permits its customers to use an online system to manage their funds.
In order to
create an account for this online system, a customer must create a 5 character PIN used for logging
in. PINs can only use the digits 09.
(a)
[5 points]
How many unique PINs can be generated using the requirements set by the bank?