Question

How many bit strings of length eight contain either three consecutive 0s or four consecutive 1s?

Answer 1

First let us compute the number of bit strings with 3 consecutive 0's.
3 consecutive 0's can start at position 1, 2, 3, 4, 5, or 6 (as there are total eight positions).
Starting at position 1: (strings of form 000xxxxx)
Remaining 5 positions can be anything, count = 25 = 32.