How many 8 bit strings either start with a 1 or end with a one?

How many 8 bit strings either start with 100 or have the fourth bit a 1?

I know that the answer is 2^5 + 2^7 - 2^4 The first term is the number of strings with 100 the second term is the number of strings with 1 as 4th bit but why is 2^4 the number in which both occur??? Is it simply that there are 2^4 ways to choose four positions???? Thank you all for looking and trying to help my old brain think in new ways.