I will give some classes in combinatorics to high school students and I would like to know some facts (and proof) I can show to my students to motivate them to study this beautiful subject.
I'm thinking to talk about this: 15 Things More Likely to Happen than Winning Mega Millions.
The problem is I don't know how to calculate these facts and I'm looking for interesting real life problems to solve with my students. So my question is do you know some interesting real life problems I could show and proof to my students?
Thanks
Best Answer
To calculate those facts, you would need some statistics. For example, to calculate the death by vending machine problem, you would need statistics on how many people each year use vending machines, and how many die from vending machines. For high school students, I think it would be cool to arrange the seats in a circle and have them experiment on the number of of different ways they could sit in it, and then show them the possibilities using combinatorics. Another proof you could do would be of Pascal's Rule. It is a simple proof requiring little knowledge of combinatorics, and would be easy for the high school students to understand. Good Luck!