How many bit strings of length 10 either begin with 5 consecutive 0's or 5 consecutive 1's?

Question

How many bit strings of length 10 either begin with 5 consecutive 0's or 5 consecutive 1's?

That is : 00000_ _ _ _ _ or 11111_ _ _ _ _

Im way to tired, im sure it is simple but my brain is dead. :(

I understand what you are saying.. just think of [00000] = 1 bit and _ _ _ _ _ = 5 bits which is 2^6. I totally knew that , heh its to late in the morning to be doing this stuff... haha

Answer 1

2^6

Just think of it as a 6 bit binary number. 5 of the bits are from the blanks, and the 6th bit (the leftmost bit) is either 0 or 1.

Answer 2

Another (closely related) answer would be -- there are two ways to pick the first five bits and 32 to pick the last five, and the choices are independent, so the answer is 2 x 32.