You have a stick of 7 interlocking cubes (or a tower of 7 Lego blocks). You cannot change the order of the cubes.
You break off a bit of it leaving it in two pieces.
Here are three of the ways in which you can do it:
In how many different ways can it be done?
Now try with a stick of 8 cubes and a stick of 6 cubes:
Now predict how many ways there will be with 5 cubes.
Try it! Were you right?
How many ways with 20 cubes? 50 cubes? 100 cubes?
ANY number of cubes?