This question concerns bit strings of length six. These bit strings can be divided up into four types depending on their initial and terminal bit. Thus the types are: 0XXXX0, 0XXXX1, 1XXXX0, 1XXXX1.
How many bit strings of length six must you select before you are sure to have at least $4$ that are of the same type? (Assume that when you select bit strings you always select different ones from ones you have already selected.)