Question about Red Black Trees

Question: If a Red-Black tree has greater than 1 node, it is guaranteed to have at least 1 red node...why? 

I am currently in the field and working on my Masters degree in CS. This is a question I encountered and could not verify the answer to. From the research I have done, this is what I have come up with:

When you insert the root, it is initially red, but recolored to black (rule: root must be black). After this, the next node will be inserted to the left or right, it will be colored red. After this, there is no case of re-coloring or rotation that will reduce the number of red nodes to zero.

Any verification/help would be much appreciated.

Thank you in advance.

@blowdart:

Actually that's not exactly correct. Red nodes must have black leaves, but black nodes can have black leaves too, so:
          b
    b          b
 r     r     r    r
b b b b b b b b

is a valid tree.
Infact:
          b
    b          b
 b    b    b    b
b b b b b b b b
 would be a valid tree, except that it will never happen.

Also:
         b
    r          b
 b    b    r     r
b b b b b b b b
is also valid.

The second tree will never happen because the rotation plus required color changes will guarantee the creation of a red node under certain circumstances in such a way that you will always have at least one red node.

That's the question. Also, I think I can explain the answer. But I want to think about it;)