Discrete Mathematics Project

Counting Techniques Probability


"TAXI!!" (Ed Snyder)


1. Students will discover different methods of using probability.

2. Students will explore different ways of tracking and recording probability.


This activity is designed for students to discover the concept of a probability as well as become familiar with the concepts of permutations and combinations.

Problem Statement

Introduce to students the concepts of permutation and combinations. Suggest to the class that taxi cab drivers often take several different routes in order to reach the same destination. There are generally many contributing factors as to which route they will take. This activity will allow students to explore and apply probability as well as, explore different techniques in organizing data.

Instructor Suggestions

1. Begin by discussing the problem statement.

2. Have students form small groups.

3. Distribute "TAXI!!" activity sheet

4. Have each group select a spokesperson to report their findings to the class.

5. Discuss students results as it relates to election theory.


"TAXI" activity sheet, chalk board, overhead projector and transparencies.


Introduction (5 min.), group work (25 min.), presentations of group work and class discussion (20 min.).

Mathematics Concepts

Discrete Mathematics Concepts

Counting techniques, probability, permutation combinations and graph theory

Related Mathematics Concepts

Probability and graphing

NCTM Standards Addressed

Problem solving, Communications, Reasoning, Discrete Mathematics.

Colorado Model Content Standards Addressed

Number Sense (1), Data Collection and Analysis (3), Geometric Techniques (4), Problem Solving Techniques (5), Linking Concepts and Procedures (6)

Curriculum Integration

This activity can be integrated into an Algebra I or Integrated I math curriculum as an introduction to probability.

Further Investigation

The assignment can be extended by figuring out different routes from one place to another on a map.



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

Kenney, M.J., & Hirsch, C. R. (Eds.). (1991). Discrete mathematics across the curriculum, K-12. Reston. VA; National Council of Teachers of Mathematics.

Last updated January 15, 1997