Help designing fun lesson plan with permutations, combinations, etc

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srfriggen
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Hello everyone,

I am an aspiring math teacher taking a workshop type class and in two weeks my group will be teaching the other students various topics on probability. We are trying to come up with a fun and interactive way to teach the counting principle, permutations, and combinations. To give you an example of other activities, for geometric probability we are doing a large game of Battleship where the class will be split into two teams and only be allowed to "fire" upon the other team after answering review questions and questions relating to geometric probability. Geometric probability falls naturally into battleship and we foresee this playing out in a very fun and energetic way.

I cannot say the same for any of the ideas we've tried to come up with for counting. Normally, in a class setting, with these topics, I would see no problem with lecturing a little and having students complete activity sheets, but the point of this class is to go all out and be as creative as we can for the days we are teaching our peers.

Can anyone think of anything fun and original that could work to teach one or more of these concepts (counting principle, permutations, combinations). The class is usually expected to split into groups of 3 or 4.
 
on Phys.org
If the students can do algebra, introduce them to generating functions by solving problems about "How many ways can you make change for a... using ...".

To me it is more pleasant to see the general principle of generating functions before seeing the binomial theorem and the binomial coefficients as a special case.
 
There are a lot of counting problems in gambling and other things. I don't know how original these are: Odds of winning the lottery. Odds of poker hands. Odds of guessing all the NCAA basketball playoff games correctly. Odds of guessing someone's random password using a variety of password strength rules. Odds of two people in the class having the same birthday.