Math 142 - Finite Mathematics Sample Exam 1 - Set Theory ...

Math 142 - Finite Mathematics
Sample Exam 1 - Set Theory & Counting
1. U = {0, 1, 2, 3, ..., 10} A = {1, 3, 5, 7, 9}
B = {2, 4, 6, 8, 10} C = {1, 4, 5, 6, 9}
Find each of the following:
a. b.
c. d.
e.
2. One hundred eighty-nine chili lovers were surveyed. One hundred thirty-two put crackers
or cheddar cheese in their chili. One hundred five put crackers in their chili. Eighty-three
put cheddar cheese in their chili. How many put crackers and cheddar cheese in their
chili?
3. A survey of 600 women was conducted to determine magazine readership. The following
was collected from the survey: 206 read Ladies Home Journal, 141 read McCall’s, 184
read Reader’s Digest, 42 read Ladies Home Journal and McCall’s, 65 read Ladies Home
Journal and Reader’s Digest, 57 read McCall’s and Reader’s Digest, 19 read all three
magazines.
How many women read...
a. at most one of the magazines surveyed?
b. exactly two of the magazines surveyed?
c. only Reader’s Digest?
d. none of the magazines surveyed?
4. A local restaurant offers twelve cocktails, seven appetizers, three salads, five main dishes,
eights side dishes, and four desserts. If a meal consists of 1 cocktail, 1 appetizer, 1 salad,
1 main dish, 2 side dishes (the same or different), and 1 dessert; how many meals does the
restaurant serve?
5. The Math and Science Club has twenty-four members. They need to elect four officers
for the current school year. In how many ways can they elect their officers?
6. In a literature class, you must read six novels from a list of 19 approved novels and pass a
written exam on each. In how many ways can you select the novels you will read?
7. The starting five of the men’s basketball team, the starting five of the women’s basketball
team, and the starting six of the women’s volleyball team bought a row of tickets to the
opening night performance of Bus Stop. In how many ways can they be seated if team
members wish to sit together?
8. An exam consists of 15 questions of which 10 must be answered. In how many ways can
the 10 questions be answered if exactly two of the first three questions must be answered?
9. How many unique arrangements can be formed from the letters in
T H O M A S J E F F E R S O N
10. Pizzeria Italiano makes a plain Mozzarella cheese pizza for $5.95. You can add sausage,
pepperoni, hamburger, Canadian bacon, mushrooms, peppers, onions, olives, Asiago
cheese, Parmesan cheese, Monterey Jack cheese, and pineapple for an extra charge. How
many different pizzas are sold?

Answer Key
1. a. {4 , 6}
b. {1 , 4 , 5 , 6 , 9} or C
c. {0 , 1 , 3 , 5 , 7 , 9}
d. {0 , 2 , 8 , 10}
e. {3 , 7}
2. 56
3. a. 474
b. 107
c. 81
d. 214
4. 322,560
5. 255,024
6. 27,132
7. 62,208,000
8. 1,485
9. 8.1729648 x 10 10
10. 4,096