Question

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 6 that are of the same type? (Assume that when you select bit strings you always select different ones from ones you have already selected.)

Answer 1

Answer:

You must select at least 21 strings of length 6.

Step-by-step explanation:

There are 2⁴ = 16 strings of each type.

Since there are 4 types of strings, then in order to have 6 strings of the same type you need to have at least 21 strings selected. The worst case will that there are 5 strings for each of the other 3 types.