Permutations and Combinations

I have to put together an assignment (problem-solving and modelling) for Year 11 students who have just studied counting techniques including permutations and combinations. Students already have a knowledge of basic probability. I want the assignment to be open-ended but must require the use of Ps and Cs in the solution. They will have a few weeks to put it together. Any ideas? (I'm not after test type questions.)

Re: Permutations and Combinations

Choose a problem that is way too advanced for them, like a Markov process. Then, have them solve the problem with you walking them through it all. So, it is one long problem, but some of the middle steps that would be too advanced are filled in already.

Or how about problems from real life? How long (on average) would it take a hacker to brute force a password? Or possibly a genetics question. Or a gambler's ruin type question.

Re: Permutations and Combinations

Quote:

Originally Posted by

**Debsta** I have to put together an assignment (problem-solving and modelling) for Year 11 students who have just studied counting techniques including permutations and combinations. Students already have a knowledge of basic probability. I want the assignment to be open-ended but must require the use of Ps and Cs in the solution. They will have a few weeks to put it together. Any ideas? (I'm not after test type questions.)

If your year 11 students do inclusion/exclusion then derangements are a good topic to explore.

Ex. Letters addressed to each of sixteen mathematics lecturers arrive. They are handed to a student worker to put into the correct post box. Being the end-of-the-day, the worker simply put each letter into one of the sixteen boxes without looking at & matching the name. How many ways can no letter be in the correct box?