Let's see, I will not give a solution here but tell you an idea. Try the idea and tell me if you have problems.

You must be learning this in recurrence relations.

Have you solved it for 2D??

That is...

Given a plane and 'n' lines on it(of which no two are parallel and no three meet at the same point), tell me how many regions does it divide the plane into???

Hint: Imagine the plane being divided by 'n-1' lines and it has regions. Now ask yourself how many additional regions will the new line divide our old regions into?? Say it is 'k' (hey you have to find this )

then . Now solve the relation.

So find 'k' on your own.

If you do this, extending it to 3D involves nearly the same procedure

So let me know your progress