How many bit strings of length 12 contain the substring 111000?

448 strings

Explanation:

Each bit string can be filled by two ways either 0 or 1. If the bit strings of length contain the substring '111000' we therefore need a substring of length 6.

The selection of bits starts from the 1st bit to 7th bit enclosing the substring 111000 and ensuring that the length 6 are all filled. So, there will be  7 ways to contain this substring.

The total ways to contain this substring = 7*2^6 =448

Therefore 448 strings of length 12 contain the substring '111000'.