Test Paper: Counting Methods and Probability Theory 
Chapter 11: Counting Methods and Probability Theory
Test Review
Name___________________________________
Date________________
Solve the problem by applying the Fundamental Counting Principle with two groups of items.
1) A restaurant offers 8 entrees and 9 desserts. In how many ways can a person order a two-course meal?
2) An apartment complex offers apartments with four different options, designated by A through D.
1)
2)
A = number of bedrooms (one through four)
B = number of bathrooms (one through three)
C = floor (first through fifth)
D = outdoor additions (balcony or no balcony)
How many apartment options are available?
3) You are taking a multiple-choice test that has 12 questions. Each of the questions has 5 choices, with one correct choice per question. If you select one of these options per question and leave nothing blank, in how many ways can you answer the questions?
3)
4) License plates in a particular state display 2 letters followed by 4 numbers. How many different license plates can be manufactured? (Repetitions are allowed.)
4)
Use the Fundamental Counting Principle to solve the problem.
5) There are 9 performers who are to present their acts at a variety show. How many different ways are there to schedule their appearances?
6) There are 4 performers who are to present their acts at a variety show. One of them insists on being the first act of the evening. If this request is granted, how many different ways are there to schedule the appearances?
Evaluate the factorial expression.
7!
7)
5!
5)
6)
7)
8)
600!
599!
8)
9)
8!
(8 - 5)!
9)
Use the formula for nPr to evaluate the expression.
10) 9P3
10)
Use the formula for nPr to solve.
11) A church has 10 bells in its bell tower. Before each church service 4 bells are rung in sequence. No bell is rung more than once. How many sequences are there?
1
11)
12) A club elects a president, vice-president, and secretary-treasurer. How many sets of officers are possible if there are 9 members
Test Review
Name___________________________________
Date________________
Solve the problem by applying the Fundamental Counting Principle with two groups of items.
1) A restaurant offers 8 entrees and 9 desserts. In how many ways can a person order a two-course meal?
2) An apartment complex offers apartments with four different options, designated by A through D.
1)
2)
A = number of bedrooms (one through four)
B = number of bathrooms (one through three)
C = floor (first through fifth)
D = outdoor additions (balcony or no balcony)
How many apartment options are available?
3) You are taking a multiple-choice test that has 12 questions. Each of the questions has 5 choices, with one correct choice per question. If you select one of these options per question and leave nothing blank, in how many ways can you answer the questions?
3)
4) License plates in a particular state display 2 letters followed by 4 numbers. How many different license plates can be manufactured? (Repetitions are allowed.)
4)
Use the Fundamental Counting Principle to solve the problem.
5) There are 9 performers who are to present their acts at a variety show. How many different ways are there to schedule their appearances?
6) There are 4 performers who are to present their acts at a variety show. One of them insists on being the first act of the evening. If this request is granted, how many different ways are there to schedule the appearances?
Evaluate the factorial expression.
7!
7)
5!
5)
6)
7)
8)
600!
599!
8)
9)
8!
(8 - 5)!
9)
Use the formula for nPr to evaluate the expression.
10) 9P3
10)
Use the formula for nPr to solve.
11) A church has 10 bells in its bell tower. Before each church service 4 bells are rung in sequence. No bell is rung more than once. How many sequences are there?
1
11)
12) A club elects a president, vice-president, and secretary-treasurer. How many sets of officers are possible if there are 9 members