Investigate!

Suppose you have some number of identical Rubik's cubes to distribute to your friends. Imagine you start with a single row of the cubes.

1. Find the number of different ways you can distribute the cubes provided:

   1. You have 3 cubes to give to 2 people.

   2. You have 4 cubes to give to 2 people.

   3. You have 5 cubes to give to 2 people.

   4. You have 3 cubes to give to 3 people.

   5. You have 4 cubes to give to 3 people.

   6. You have 5 cubes to give to 3 people.

2. Make a conjecture about how many different ways you could distribute 7 cubes to 4 people. Explain.

3. What if each person were required to get at least one cube? How would your answers change?