Discrete Mathematics Project

Counting Techniques Activity


Buy Me Some Peanuts And Crackerjacks (Jill Long)


Students will explore the concepts of permutation, combination, and probability.


This activity allows the student to work with the concepts of permutation, combination, and probability in a familiar setting. Students will be able to decide which counting technique is appropriate for each individual setting.

Problem Statement

This activity doesn't need much set-up. You could talk about Coors Field and the Rockies and get a little discussion going with the students who have been there, etc. This activity could be used as an introduction to see if they can come up with a sufficient answer, or it could be used as a quick practice to review.

Instructor Suggestions

1) Discuss problem statement with class as a whole.

2) Have them work in pairs or in groups, depending on the goal of the activity. Is it a discovery type of activity or a review?

3) Just let them work without much guidance, or without giving them many hints.

4) Have groups present their strategies to the class.




intro ( ~5 min), work time (10-20 min), presentations (5-10 min)

Mathematics Concepts

Discrete Mathematics Concepts

permutation, combination, probability, addition principle, factorial, mutually exclusive events

Related Mathematics Concepts


NCTM Standards Addressed

Problem solving, communication, reasoning, connections, algebra, probability, discrete mathematics

Colorado Model Content Standards Addressed

Algebraic Techniques (2), Problem Solving Techniques (5), Linking Concepts and Procedures (6)

Curriculum Integration

There seems to be a unit or mention of probability in every high school math class. It could be used when discussing permutations and combinations. It is probably too simple of a task to use as a problem of a week in any class above geometry.

Further Investigation

Many other questions could have been asked here. For instance, what happens if three people go to get drinks, etc. instead of two?



Algebra 2 and Trigonometry. (1991) McDougall Littell & Company.

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

Last updated January 16, 1997