# What are some good ideas in teaching combinations and permutations

I am a student teacher trying to brainstorm some effective lesson plans for combinations and permutations for a high school statistics course. My master teacher has decided that he will introduce combinations, so I'm left with presenting counting problems involving permutations with nondistinct items and probabilities involving combinations. For example, by the end of the lesson I expect the students to find the total number of distinct arrangements of the word TATTER. I also expect them to solve problems like these:

A manufacturing site produces 120 computers, 4 of which are defective. The quality control manager selects 5 computers. What is the probability that exactly one of them is defective?

In this problem, I expect them to reason that they need 1 defective computer from 4 defective computers: $\binom{4}{1}$ and that the number of choosing 4 nondefective computers from 116 is $\binom{116}{4}$. They are then supposed to use the multiplication rule and then divide the result by $\binom{120}{5}$.

What activities/worksheets/teaching strategies would be helpful for this lesson? I've looked up on-line and there aren't that many resources available. The target audience are 11th/12th graders who at least passed Algebra II with a C and Precalculus with a D.

My main concern is the presentation of the materials. Many of them are expected to have problems with manipulating with factorial expressions and a significant % are developmentally not ready yet to handle questions that seem open-ended or ask for something that requires additional thinking beyond the lesson. The majority of them are familiar with teachers showing them how to do a math problem and then copying a procedure to similar questions.

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