Permutations and Combinations

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In this activity, students review some probability (particularly area and tree diagrams as a means for solving probability problems) and then delve into a series of inquiry-based problems that lead to a deeper understanding of counting principles. Students will
  • Use area diagrams and tree diagrams to find and explain probabilities
  • Develop systematic lists for complex situations
  • Use the multiplication principle for choosing one element from each of several sets
  • Define and use the concepts of permutation and combination
  • Understand and use standard notation for counting permutations and combinations
  • Develop formulas for the permutation and combinatorial coefficients

Instructions for Students

This is designed as a self-paced activity; in other words, there are no deadlines. The only expectation concerning time is that you use spare class time on making progress on these handouts. You may work on your own, but you must check your approaches with at least one other person (which could be a friend, a peer, me, another teacher or an academic coach).

You are highly encouraged to do the first three handouts, since they are what we are learning to do in class. If you are not sure how to get the correct answers to the review problems, you must also follow the probability work we are doing in class.

Working individually or with a small group of people, attempt each question in the handouts. If the question is not clear or you are not sure how to get started, you must get help. Use available class time and my office hours, as necessary, to make progress.

Once you have completed all questions on a handout, check your answers (yes, they are posted to the left). If you got any questions wrong, first try to use the answer to help you find your mistake. If you cannot correct your mistake, then you must get help. Do not move on to the next handout until you understand at least one approach for answering all the questions on your current handout (the handouts are designed to build on what you learned from the previous handout).

If you are working in a group, be sure to remain open to the ideas of everyone in your group: these problems can be approached in more than one way and it's very important that everyone's approach be considered. If you are working alone, again, you must check your approaches with at least one other person.