College Algebra
Answer/Discussion to Practice Problems Tutorial 55: Fundamental Counting Principle
Answer/Discussion
to 1a
One quarter, one dime and one sixsided die are tossed. How many
results are possible? 
Let's use the basic counting principle:
There are 3 stages or events: one quarter, one dime, and one sixsided
die.
Each coin has 2 possible outcomes, either a tail or a head.
The die has 6 possible outcomes.
Putting that all together we get:
quarter


dime


die


# of possible outcomes

2

x

2

x

6

=

24

So there are 24 different possible outcomes. 

Answer/Discussion
to 1b
Next semester you are going to take one science class, one math class,
one history class and one english class. According to the schedule
you have 4 different science classes, 3 different math classes, 2 different
history classes, and 3 different English classes to choose from.
Assuming no scheduling conflicts, how many different fourcourse selections
can you make? 
Let's use the basic counting principle:
There are 4 stages or events: a science class, a math class, a history
class and an english class.
There are 4 different science classes, 3 different math classes,
2 different history classes, and 3 different English classes to pick
from.
Putting that all together we get:
Science


Math


History


English


# of schedules

4

x

3

x

2

x

3

=

72

So there are 72 different schedules possible. 
Answer/Discussion
to 1c
Six students in a speech class all have to give there speech on the
same day. One of the students insists on being first. If this
student's request is granted, how many different ways are there to schedule
the speeches? 
Let's use the basic counting principle:
There are 6 stages or events: speaker 1, speaker 2, speaker 3,
speaker 4, speaker 5, and speaker 6.
There is only one possibility for speaker 1.
That leaves 5 possibilities for speaker 2, which leaves 4 for speaker
3, which leaves 3 for speaker 4, which leaves 2 for speaker 5 which leaves
1 for speaker 6.
Putting that all together we get:
speaker 1


speaker 2


speaker 3


speaker 4


speaker 5


speaker 6


# of ways

1

x

5

x

4

x

3

x

2

x

1

=

120

So there are 120 different ways they can be scheduled to speak. 

Last revised on May 16, 2011 by Kim Seward.
All contents copyright (C) 2002  2011, WTAMU and Kim Seward. All rights reserved.

