Try and get the students to calculate how many ways 4 people can shake hands. This is the same as how many ways they can communicate. Get them to draw it. Then show if you join each point up to the other it visually gives you the answer.

Get them to create mystic rose patterns to reflect the possibilities for communication. This shows how 12 people can communicate.

I particular like doing this exercise with pegs and wool to create structures in real life. How many presents will a family of 12 give and receive?