Draw a 'doodle' - a closed intersecting curve drawn without taking pencil from paper. What can you prove about the intersections?
I want some cubes painted with three blue faces and three red faces. How many different cubes can be painted like that?
A player has probability 0.4 of winning a single game. What is his
probability of winning a 'best of 15 games' tournament?
In how many ways can two, four or six people to be arranged in this way for a photo, or eight people? In how many ways can the ten team members be arranged like this for the photo to be taken?
You may even like to generalise the problem to twelve people or to any specified even number.
Now try the problems Walkabout and Counting Binary Ops