Discrete Mathematics Project

Counting Techniques Activity


The Raffle (Jill Long)


Students will begin to use the multiplication and addition principles when working with probabilities.


This activity, which is set to occur sometime before Prom, asks the students to find the probabilities of winning a number of prizes given that they have bought a set number of tickets. This activity could be used after they have been introduced to the multiplication and addition principles.

Problem Statement

Talk about the after-Prom. There really will be a raffle there. What do they think are their chances of winning? How many tickets will they buy to increase their odds? Let's look at an example as a class to see if it can help you raise your chances of actually winning a prize.

Instructor Suggestions

1) Set the stage with the problem statement.

2) Have them work in groups of 4, not dividing the problems up, but having everyone work together to come up with a strategy that the group will use.

3) Be flexible. If one group wants to change the number of tickets that they purchased, let them. It might promote a good discussion.

4) Have the groups come up to present findings and strategies.


handout, calculators would be nice


introduction (5 min), group work (25 min), presentation (10 min)

Mathematics Concepts

Discrete Mathematics Concepts

Counting Techniques, probability, permutations, combinations, independent vs. dependent events, multiplication principle, addition principle

Related Mathematics Concepts


NCTM Standards Addressed

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

Colorado Model Content Standards Addressed

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

Curriculum Integration

This activity could be integrated into an Algebra 2 class when talking about probabilities, permutation, etc. Any class above an Algebra 2 class could use this as well.

Further Investigation

This activity might be better if you let each group actually pick the number of tickets that they will buy, and discuss the money spent versus the greater chances of winning.



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