Discrete Mathematics Project

Counting Techniques Activity


How Many is That? (Liz Sansone)


Students will explore the concepts of permutations and combinations


Students are asked to work alone and then in a small group, encountering approaches to different counting techniques and the differences between permutations and combinations. .

Problem Statement

Discuss with your students the idea that there are many different ways to do many different things (i.e., watch t.v, do hw, take shower or the other way around, etc.). Remind them to be aware of when two things are really the same.

Instructor Suggestions

1) Discuss "Problem Statement" from above with your students.

2) Have students work alone for 5-7 minutes then get together in small groups to discuss.

3) Distribute "How Many is That" activity sheet, also distribute a transparency and a marker to each group, one person needs to illustrate the groups' approach..

4) When the small groups are finished, have a spokesperson for each group share their method using the transparency that they prepared.

5) Discuss the students' work and discuss the difference between the two types of grouping.


How Many is That? activity sheet, transparencies, markers.


Introduction (5 min.) individual work (5-7 min.) small group work (10 min.), presentation of small group work and large group discussion (20 min.).

Mathematics Concepts

Discrete Mathematics Concepts

Counting techniques, permutations, combinations

Related Mathematics Concepts

data representation

NCTM Standards Addressed

Problem Solving, Communication, Reasoning, Connections, Algebra, Geometry, Discrete Math.

Colorado Model Content Standards Addressed

Data Collection and Analysis (3), Problem Solving Techniques (5), Linking Concepts and Procedures (6)

Curriculum Integration

This activity could be integrated into a traditional or Integrated Algebra 1 class as the topic of .counting techniques is introduced. This will be a simple intro to the difference between permutations and combinations.

Further Investigation

Extend the problem by using other situations that have the same number to choose from but where one situation would be considered repeats so students can see when they need to divide out for duplicates



Crisler, N., Fisher, P., & Froelich, G. (1994). Discrete mathematics through applications. New York: W.H. Freeman and Company.

Last updated January 16, 1997