This Nrich Lottery Simulator was a great way to introduce Combinations and Permutations to my Stats class. We started with students choosing 1 number out of a possible 4 to see who could win (and several did). I then allowed them to choose from 5 numbers. Fewer students won. Then I asked them to pick 2 numbers between 1 and 5. Even fewer won.
Then, following the British National Lottery, they had to choose 5 numbers between 1 and 49. A couple got 2 numbers correct at most. This led nicely into a conversation about how many combinations are possible, whether order matters and how we can work these things out. They were also hooked for the whole time.
This also helped to convince them that their chances of winning anything on the lottery were very slim. I think this will also lead very nicely into talking about expected value.
Pumphrey's Math 